Question

M & M's offers customers the opportunity to create their own color mix of candy. There are $21$colors to choose from and 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 and$6$different colors are chosen?

Short answer

The answer is$39,070,080.$

Step-by-step solution

Step 1. Given information.

Total colors are$21$to choose colors are$6.$

Step 2. Calculation.

There are total $21$colors and we have to choose $6$different colors without repetition. Since we select a color then a number will less from the total number.

Thus,

$21\times 20\times 19\times 18\times 17\times 16=39,070,080.$