Question

Suppose that a group of 10 students are to be assigned to four dorm rooms: a single, a double, a triple and a quad. How many ways are there are making the assignments? Choose the best answer.

Answer 1

Total number of ways to select all sstudent to make assignment = 10×36×70×1 = 25200

Explanation:

We have given number of students = 10

These 10 students are assigned to four dorm rooms a single, a double, a triple and a quad

So number of ways to assigned single student
`=^(10)C_1=(10!)/(1!9!)=10\\`

Now left student = 10 -1 = 9

So number of ways to assigned double student
`=^(9)C_2=(9!)/(2!7!)=36`

Now left student = 9-2 = 7

So number of ways to assigned triple student
`=^(7)C_3=(7!)/(2!4!)=`=70

Now left student = 7 - 3 = 4

So number of ways to assigned quad student
`=^(4)C_4=(4!)/(4!0!)=1`

So total number of ways to select all sstudent to make assignment = 10×36×70×1 = 25200