Question

There are 14 tops you’d like to purchase, but you can only afford six. If you select tops at random, how many different groups of six tops could you select?

Answer 1

3003 different groups of 6tops

Explanation:

Using the combination formula, generally, when selecting r number of objects out of a pool of n numbers, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

If there are 14 tops I'd like to purchase and I can only afford six, the number of ways I can choose this six at random from the 14tops can be done in 14C6 number of ways.

14C6 = 14!/(14-6)!6!

14C6 = 14!/8!6!

14C6 = 14×13×12×11×10×9×8!/8!×6×5×4×3×2

14C6 = 14×13×12×11×10×9/6×5×4×3×2

14C6 = 14×13×12×11/8

14C6 = 3003ways