Apaint 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.

a

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.