Question

I am trying to figure out how to complete the following problem:

M&Ms offers customers the opportunity to create their own color mix of candy. There are 21 colors to choose from, & customers are allowed to select up to 6 different colors. How many different color mixes are possible, assuming that no color is selected more than once?

Answer 1

How many choices are there for the first color?

Answer 2

Once that is chosen, how many choices are there for the 2nd color?

Answer 3

Combinations: http://www.mathwords.com/c/combination_formula.htm

From 21 colours, choose 6:
\[\Large 21C6 = \frac{ 21! }{ 6! (21-6)! }\]

Or do it the way @DebbieG is hinting at.

Answer 4

Right, they are equivalent because mine will come up with the same expression as @agent0smith . Either will work, but it's definitely good to know the combinations formula. With many more than 6 "slots" of items, it would be easier than just punching through the product. :)

Answer 5

the answer should end up being 54,264, but I'm not getting that for some reason?

Answer 6

if you use @agent0smith 's formula you will. If you use mine, you have to divide out all the combinations that are the same. E.g., it is the same combination if you pick red then yellow as if you pick yellow then red.

That's why it's a Combination, not a Permutation. Because the order in which you pick the colors doesn't matter.

Answer 7

I get the answer you gave, using the Combinations formula.

Answer 8

thank you