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.

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aristeus aristeus · Answer 1 · 2020-01-02T07:14:22+01:00

Answer:

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

Step-by-step 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 [tex]=^{10}C_1=\frac{10!}{1!9!}=10\\[/tex]

Now left student = 10 -1 = 9

So number of ways to assigned double student [tex]=^{9}C_2=\frac{9!}{2!7!}=36[/tex]

Now left student = 9-2 = 7

So number of ways to assigned triple student [tex]=^{7}C_3=\frac{7!}{2!4!}=[/tex]=70

Now left student = 7 - 3 = 4

So number of ways to assigned quad student [tex]=^{4}C_4=\frac{4!}{4!0!}=1[/tex]

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