Answer:
792
Step-by-step 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 : [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
n = 12
r = 7
Substitute the given values :
[tex]^{12}C_7=\frac{12!}{7!(12-7)!}[/tex]
[tex]^{12}C_7=\frac{12 \times 11\times 10 \times 9\times 8\times 7! }{7!(5)!}[/tex]
[tex]^{12}C_7=\frac{12 \times 11\times 10 \times 9\times 8}{5 \times 4\times3\times2\times1}[/tex]
[tex]^{12}C_7=792[/tex]
Thus there are 792 ways in which seven time slots can be assigned.
