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?

220 color combinations are possible.

Step-by-step 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.

220 combinations.

Step-by-step 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.