There are 100 students at a school and three dormitories A, B, and C with capacities of 25, 35, and 40, respectively.

Required:
a. How many ways are there to fill up the dormitories?
b. Suppose that, of the 100 students, 50 are men and 50 arewomen and that A is an all-men's dorm, B is an all-women's dorm andC is co-ed. How many ways are there to fill thedormitories?

Answers

Answer 1

Answer:

a

[tex]N = 7.0 *10^{44} \ Ways [/tex]

b

[tex]U  = 2.85 *10^{26}\  ways [/tex]

Step-by-step explanation:

From the question we are told that

   The number of students are  n =  100

    The number of dormitories  is  k =  3

    The capacity of the first dormitory is  A =  25

     The capacity of the second dormitory is  B =  35

      The capacity of the third dormitory is  c =  40

Generally the number of way to fill the dormitory up is mathematically represented as

      [tex]N  =  \frac{n!}{A! B!C!}[/tex]

=>   [tex]N  =  \frac{100!}{25! 35! 40!}[/tex]

Here ! stands for factorial, so we will be making use of the factorial functionality in our calculators to  evaluated the above equation

=>   [tex]N  =  \frac{100!}{25! 35! 40!}[/tex]

[tex]N = \frac{9.332622* 10^{157}}{[1.551121* 10^{25}]* [1.0333148* 10^{40}] * [8.1591528*10^{47}]}[/tex]

[tex]N = 7.0 *10^{44} \ Ways [/tex]

From the question we are told that there are 50 men and  50  women and

     A is  all-men's dorm and  B is all-women's dorm while C is co-ed

So

When A is filled , the number of men that will be remaining to fill dorm C is  50-25 = 25

While when B is filled the number of women that will be remaining to fill dorm C is   50-35 = 15

Generally the number of ways there to fill the dormitories is equivalent to the number of ways of selecting the 25 men and 35 women to fill dormitory A and B plus one more way which is filling dorm C with the remaining students this is  mathematically represented as  

       [tex]U  =  ^{50}C_{35} * ^{50}C_{25}  +  1[/tex]

Here C stands for combination hence we will be making use of the combination functionality in our calculators

     [tex]U  = 2.250829575* ^{12}  * 1.264106064 * 10^{14} +  1[/tex]

=>    [tex]U  = 2.85 *10^{26}\  ways [/tex]

     


Related Questions

divide and answer in simplest form: 1/3 divided by 5

Answers

Answer:

1/15

Step-by-step explanation:

1. You can divide 1/3 by 5 by changing the division symbol to its reciprocal, multiplication, and also divide by the reciprocal of the number after the symbol, 5. The reciprocal of 5 is 1/5.

2. Now you can do 1/3 multiplied by 1/5. Multiply the numerators by the denominators. The numerators are 1 and 1, so you multiply 1 by 1 which equals 1. Now you multiply the denominators, 3 and 5, which is equal to 15. If the numerator is now 1, and the denominator is 15, the new fraction is 1/15, getting you to your answer

Micah found the least common multiple of 8 and 12. His work is shown below.

Multiples of 8: 8, 12, 16, 20, 24, 28, . . .
Multiples of 12: 12, 24, 36, 48, 60, . . .

The least common multiple is 12.

What is Micah’s error?

Answers

Answer:when he was doing the multipleis of 8 he put 20 when there is no 20

Step-by-step explanation:

He forgot the 20 when he was doing the 8

A famous recipe for New Orleans jambalaya calls for 1 1/4 cups of Gulf shrimp. The recipe serves 5 people. Trinetta and Agnes want to serve 12 people, so they increase all the ingredients proportionally. How much Gulf shrimp is required for the new recipe?

A. 1 2/5
B. 5/12
C. 3 cups
D. 4/5 cups
E. 7 cups​

Answers

Answer: C. 3 cups

Step-by-step explanation:

Given: In recipe for 5 people, Required Gulf shrimp = [tex]1\dfrac14[/tex] cups

Since, [tex]1\dfrac14=\dfrac{5}{4}[/tex]

Required Gulf shrimp = [tex]\dfrac54[/tex] cups

Then, for 1 people Gulf shrimp required = [tex]\dfrac{5}{4}\div 5[/tex]

[tex]=\dfrac54\times\dfrac{1}{5}[/tex]

[tex]=\dfrac14[/tex] cup

For 12 people, it is required = [tex]12\times\dfrac14 = 3\text{ cups}[/tex]

Hence, 3 cups of gulf shrimp is required for new recipe.

So, correct option is C. 3 cups

Which of the following does NOT represent a whole number?
9, 6.0, 12/4, -12/3 help plz

Answers

Answer:

-12/3

Step-by-step explanation:

Whole numbers can't be negative!

Answer:

d. your welcome

Step-by-step explanation:

Given that a=4,b=2 and c=-1, find the value of a-b+c

Answers

Answer:

1

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

a - b + c

a = 4

b = 2

c = -1

Step 2: Solve

Substitute:                         4 - 2 - 1Subtract:                            2 - 1Subtract:                            1

Suppose a​ carpenter's ruler was marked in​ thirty-seconds. What would be the fraction and its decimal equivalent for the mark on the ruler between 29/32 and 30/32​?

Answers

Answer:

the fraction and its decimal equivalent for the mark on the ruler

= 59/64 = 0.921875

Step-by-step explanation:

Given that;

A CARPENTER 's ruler is marked in thirty  seconds

mark on the ruler between 29/32 and 30/32​ is the average of the values

we know that average is the summation of all terms divided by the number of appearance of terms

so

= (29/32 + 30/32​) / 2

= ((29 + 30) / 32) / 2

= (59 / 32) / 2

= 59 / 64

= 0.921875

therefore the fraction and its decimal equivalent for the mark on the ruler = 59/64 = 0.921875

PLS HELP QUICKLY WILL GIVE BRAINLIEST

Answers

Answer:

the first one

Step-by-step explanation: it is your answer because when you solve it i gt that answer i calculated it in a calculator and then showed to the teahcre and said that it was crrect please mark me as brainlist

(30 POINTS NEED HELP FAST)
A line has a slope of 2 and goes through the point (4,−3). What is the equation of this line in Standard Form?

−2x+y=−5

2x+y=−5

−2x+y=5

−2x+y=−11

Answers

Answer: −2x+y=−11

(4,-3) = −2x+y=−11.

Answer: −2x+y=−11.

Whats the circumference of a circle object that's 2 meters ?

Answers

I think the answer is 12.57

Can someone answer this and explain how to solve the 3 with the exponent of -4?

Answers

Answer:

3⁷

Step-by-step explanation:

When you multiplying or dividing numbers with exponents, you keep the base the same and specifically with dividing, you subtract the exponents themselves. So, you would be doing 3-(-4), which is 7.

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Exponents and power,

Since we know the concept that, any power in denominator of a fraction is shows as negative power when it comes to the Numerator of the fraction,like eg:-

[tex]1 \div ( {5}^{8} ) = {5}^{ - 8} [/tex]

so we apply here same,

also

[tex]1 \div ({5}^{ - 8} ) = {5}^{8} [/tex]

so we get as,

[tex] {3}^{3} \div {3}^{ - 4} = {3}^{3} \times {3}^{4} [/tex]

this is the answer.

Main Menu
Solve the equation
Unit 2
- 8c+7= -25
Section 3.2
Section 3.3
Section 9.3
Section 9.5
Section 9.6

Answers

Answer:

c = 4

Step-by-step explanation:

Solve for"c" in the following equation:

- 8 c + 7 = - 25

Subtract 7 from both sides:

- 8 c = - 25 - 7

combine like terms

- 8 c = -32

divide both sides by "-8" to isolate c on the left

c = - 32 / (-8)

c = 4

4(1-x)+2x=-3(x+1) solve for X

Answers

Answer:

x=-7

Step-by-step explanation:

4(1-x)+2x=-3(x+1)

4-4x+2x=-3x-3

4-2x=-3x-3

-2x=-3x-7

x=-7

c. One sixth of a number is 15. What is the number?
Please explain step by step.

Answers

Answer:

90

if 15 is 1 6th then yo need 5 more 15s to find out the whole number

ah
nsjakensnsjskdkdkdjjsjsjshshsjzjs

Answers

Answer:

Step-by-step explanation:

what Mitochondria of a
of a cell

Answers

Answer:

membrane-bound cell organelles

What are the coordinates of the point (-3, 4) after a translation 5 units
right and 6 units down?

Answers

Answer:

(2,-2)

Step-by-step explanation:

Find the measures of the missing values.

Answers

1. X and Y= 39 (180-102=78, 78 divided by 2=39)

what is the measure of CED

Answers

Step-by-step explanation:

The measure of CED is p degree.

In triangle ABC and EDC,(Given)(Vertical opposite angles)

By AA rule of similarity,

Corresponding angles of similar triangles are same.

Therefore the measure of CED is p degree.

pls give brainest

Every day you collect 8 pennies and keep them in a jar. The first day you have 8, the second day you have 16, etc. How many pennies do you have on the 113th day?​

Answers

Answer:

904

Step-by-step explanation:

8 x 113 = 904

I think it is 904
Hope this helps!!!!!

HURRY ON A TIMER PLEASE HELP

which shows all the like terms in the expression ​

Answers

Answer:

the second one -3and1 :4x and 7x

Step-by-step explanation:

Answer:

-3 and -1; 4x and 7x

Step-by-step explanation:

like terms are the numbers with the same variable

eg. 4x^2 and 6x aren't like terms, but 2x^4 and 3x^4 are

please help asap :)​

Answers

The answer to this question is “No”

g Suppose you are rasterizing a triangle with vertices (1, 1), (5, 1), and (2, 9), and the intensity values (e.g., redness) of those vertices are 5, 9, and 14, respectively. Using the linear interpolation scheme, what is the intensity value of an interior point at (3, 5)? Show all your work.

Answers

Answer:

6.333

Step-by-step explanation:

Our triangle vertices are

(1,1)(5,1)(2,9)

We are to perform interpolation at point(3,5)

x and y values are interpolated

On vertices (5,1)(2,9)

x = 3

x1 = 5

X2 = 2

Y1 = 1

Y2 = 9

Formula for interpolation

Y = [y1+(x-x1)(y2-y1)]/x2-x

Y = 1+(3-5)(9-1)/2-5

Y = 1+[-2*8/-3]

Y = 1+16/3

From here we use use LCM to get:

19/3 = 6.333

Researchers recorded the speed of ants on trails in their natural environments. The ants studied, Leptogenys processionalis, all have the same body size in their adult phase, which made it easy to measure speeds in units of body lengths per second (bl/s). The researchers found that, when traffic is light and not congested, ant speeds vary roughly Normally, with mean 6.20 bl/s6.20 bl/s and standard deviation 1.58 bl/s.1.58 bl/s. (a) What is the probability that an ant's speed in

Answers

This question is Incomplete

Complete Question

Researchers recorded the speed of ants on trails in their natural environments. The ants studied, Leptogenys processionalis, all have the same body size in their adult phase, which made it easy to measure speeds in units of body lengths per second (bl/s). The researchers found that, when traffic is light and not congested, ant speeds vary roughly Normally, with mean 6.20 bl/s and standard deviation 1.58 bl/s. (a) What is the probability that an ant's speed in light traffic is faster than 5 bl/s? You may find Table B useful. (Enter your answer rounded to four decimal places.)

Answer:

0.7762

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Population mean = 6.20 bl/s

Standard deviation = 1.58 bl/s.

x = 5 bl/s

z = 5 - 6.20/1.58

z = -0.75949

The probability that an ant's speed in light traffic is faster than 5 bl/s is P( x > 5)

Probability value from Z-Table:

P(x<5) = 0.22378

P(x>5) = 1 - P(x<5)

= 1 - 22378

= 0.77622

Approximately to 4 decimal places = 0.7762

The probability that an ant's speed in light traffic is faster than 5 bl/s is 0.7762

can yall help me out please.​

Answers

Answer:

which one equals 12? option C

Step-by-step explanation:

How do I Evaluate f(5).

Answers

plug in 5 for x in your equation and solve

. An independent-measures research study was used to compare two treatment conditions with n=12 participants for each treatment. The first treatment condition had M=55 with a variance of s2=8, and the second treatment condition had M= 52 and s2=4. Look up the appropriate critical value based on your computed degrees of freedom. Do these data indicate a significant difference between the two treatments

Answers

Answer:

Decision rule  is  

Fail to reject the null hypothesis

 The conclusion is  

There is sufficient evidence that indicate that there is a significant difference between the two treatments

Step-by-step explanation:

From the question we are told that  

    The sample size is  n =  12

    The first  mean is  [tex]M_1  =  55[/tex]

    The variance is  [tex]s^2_1 =  8[/tex]

    The second mean is  [tex]M_2  =  52[/tex]

     The second variance is [tex]s^2_2 =  4[/tex]

Let the level of significance be  [tex]\alpha  =  0.05[/tex]

The null hypothesis is  [tex]H_o  :  M_1 = M_2[/tex]

The alternative hypothesis is [tex]H_a  :  M_1 \ne M_2[/tex]

  Generally the test statistics is mathematically

     [tex]t = \frac{M_1 - M_2 }{ \sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}} }[/tex]

=>   [tex]t = \frac{55 - 52 }{ \sqrt{\frac{8}{12} +\frac{4}{12 }} }[/tex]

=>   [tex]t = 1.1619 [/tex]

Generally the degree of freedom is mathematically represented as

      [tex]df = 12 -1[/tex]

=>    [tex]df = 11 [/tex]

Generally  from the t- distriibution table the critical  value  of  [tex]\alpha[/tex] at a degree of freedom of [tex]df = 11 [/tex]  is

    [tex]t_{0.05 , 11} =  2.20098516[/tex]

Here given that the critical value is greater than the t statistics value the

Decision rule  is  

Fail to reject the null hypothesis

 The conclusion is  

There is sufficient evidence that indicate that there is a significant difference between the two treatments

4. A statistician working for the National Basketball Association supplies the television announcers with interesting statistics. At a certain point in the season, he discovered that in 375 games, 300 were won by the team that was winning the game at the end of the third quarter. The margin of error in a 90% confidence interval estimate of the true proportion of games won by the team leading at the end of the third quarter with the plus-4 adjustment applied is (Show work): (5)

Answers

Answer: 0.038

Step-by-step explanation:

Given: Total games : n= 375

Number of games won by  the team that was winning the game at the end of the third quarter. = 300

The proportion (p) of the team that was winning the game at the end of the third quarter: [tex]p=\dfrac{300}{375}=0.8[/tex]

Critical z-value for 90% confidence: z* = 1.645

Margin of error =[tex]z^*\sqrt{\dfrac{(1-p)p}{n}}[/tex]

The margin of error in a 90% confidence interval estimate of p [tex]=1.645\sqrt{\dfrac{0.2\times0.8}{300}}\\= 1.645\times\sqrt{0.00053333}\\\\=1.645\times0.0231\\\\=0.0379995\approx$$0.038[/tex]

Hence, the required margin of error = 0.038

Find the x- and y-intercepts of the graph of the linear equation −4x+3y=−30

Answers

Answer:

y-int = -10, x-int = 15/2

Step-by-step explanation:

y int:

-4(0)+3y=-30

3y=-30

y=-10

x int:

-4x+3(0)=-30

-4x=-30

x=30/4=15/2

the nth term of a sequence is 20-n^2
a) find the third term of the sequence
b) which term in the sequence is the first to have a negative value ​

Answers

Answer:

a) 20 - 3^2 = 11

b) 5th, 20 - 5^2 = -5

Step-by-step explanation:

The answer assumes your terms begin at 1. If the terms begin at zero

a) 16

b) 6th term

if you chose to be extremely technical you would take the square root of 20.1 or 20.00000009 but I'm assuming they want whole numbers

Answer:

a)11

b)5th term

Step-by-step explanation:

The solution to the system -2x+5y=-15 and 5x+2y=-6 is what

Answers

Step-by-step explanation:

−2x+5y=−15 and 5x+2y=−6

Rewrite equations:

−2x+5y=−15;5x+2y=−6

Step: Solve−2x+5y=−15for x:

−2x+5y=−15

−2x+5y+−5y=−15+−5y(Add -5y to both sides)

−2x=−5y−15

−2x−2=−5y−15−2(Divide both sides by -2)

x=52y+152

Step: Substitute52y+152forxin5x+2y=−6:

5x+2y=−6

5(52y+152)+2y=−6

292y+752=−6(Simplify both sides of the equation)

292y+752+−752=−6+−752(Add (-75)/2 to both sides)

292y=−872

292y292=−872292(Divide both sides by 29/2)

y=−3

Step: Substitute−3foryinx=52y+152:

x=52y+152

x=52(−3)+152

x=0(Simplify both sides of the equation)

Answer:

x=0 and y=−3

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