Question

1. A student must select four elective courses from a total of twelve offered by the college in her major.

1. How many ways to select the four courses are possible? (order does not matter)
2. If the order in which these courses is important, in how many ways can they be selected? (in other words, how many permutations of four courses out of twelve?)

Answer 1

$\small a) C(12,4) = \binom{12}{4}=\frac{12!}{4!*8!}=495$

12! b)P(12. 4) = 4 81 * 4! = 11880

As in b) order is important that's why we multiply C(12, 4) by 4! to get total number of permutations.

Please comment if any doubt. Thank you.