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?

a

b

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

=>  

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

=>  

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  

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

=>    

i can you with this question sweetie!

step-by-step explanation: