Question

What is 13^c^11?
O A. 91
OB. 105
C. 78
D. 120

Answer 1

78

1) Since we have a Combination, we can write out the following formula:

`_(13)C_(11)=(13!)/(11!(13-11)!)=\frac{13*12*11!}{11!\text{ 2!}}=(13*12)/(2)=78`

Note that we canceled 11! on the numerator by the factorial of 11! on the denominator. And notice this is only possible when the order does not matter.

2) Hence, the answer is 78 because there are 78 combinations of 13 choosing 11.