Question

A paint box contains 12 bottles of different colors. If we choose equal quantities of 3 different colors at random, how many color combinations are possible?

Answer 1

220 combinations.

Explanation:

This will be 12C3 combinations.

= 12! / [(12-3)! 3!].

A quick mehtod to calculate this is 12*11*10 / 3*2*1

= 2*11*10

= 220.

Answer 2

220 color combinations are possible.

Explanation:

A combination is a way of selecting members from a grouping, such that the order of selection does not matter.

in our case we have 3-combinations of a set of 12 elements:

C(12, 3) = 12!/(3! (12-3)!)

C(12, 3) = 12!/(3! 9!)

C(12, 3) = (10*11*12)/(2*3)

C(12, 3) = 220 color combinations are possible.