Mike has 11 new CD's.

Let S = {s1, s2, s3, s4, s5, s6, s7, s8, s9, s10 ,s11} is the set of all the CD's Mike has.

He needs to bring 6 CD's out of 11.

One possibility for choosing a CD would be : s1 s2 s3 s4 s5 s6

We need to count all different possibilities that is, to find the number of all 6-combinations of 11 elements.

Combination is a way of selecting several things (in our case 6 CDs) out of a larger group (in our case 11 CDs), where order does not matter.

So we need to calculate C(n, k) where n = 11 and k = 6

By the formula for combinations

C(n,k) = n! / ((n-k)!*k!) where by definition n! = 1*2*....*n

we have

C(11,6) = 11! / ((11-6)!*6!)

C(11,6) = 7*8*9*10*11 / 1*2*3*4*5

C(11,6) = 462

Make has 462 possibilities for choosing CDs.