Question

Twelve students ask to visit a college admissions counselor. The counselor can meet with one student at a time. in how many ways can seven time slots be assigned?

Answer 1

If we put all the seven slots and we caculate like this:

12*11*10*9*8*7*6
Then the result will be 3,991,680

I hope this can help you

Answer 2

792

Explanation:

Given : Twelve students ask to visit a college admissions counselor. The counselor can meet with one student at a time.

To Find:In how many ways can seven time slots be assigned?

Solution:

Total number of students = 12

No. of slots = 7

Counselor can meet 1 student at one time slot.

So, to find the number of ways in which seven time slots can be assigned we will use combination:

Formula :
`^nC_r=(n!)/(r!(n-r)!)`

n = 12

r = 7

Substitute the given values :

`^(12)C_7=(12!)/(7!(12-7)!)`

`^(12)C_7=(12 * 11* 10 * 9* 8* 7! )/(7!(5)!)`

`^(12)C_7=(12 * 11* 10 * 9* 8)/(5 * 4*3*2*1)`

`^(12)C_7=792`

Thus there are 792 ways in which seven time slots can be assigned.