A bowl of candy contains many pieces of candy but only six d

A bowl of candy contains many pieces of candy but only six different types of candy. How many ways can three pieces of candy be removed from the bowl? Assume you can remove one or more pieces of the same type of candy.

Solution

We have 6 choices for your first piece.

Then for each possible option in our first choice that is 6, we have 6 more choices for our second choice.

=> our total is now 6*6=36.

Then for eachthe 36 combinations we have 6 more choices for option 3.

Hence 6 * 6 * 6=216

we now have to exclude the duplicates results (for example we already have 1-1-2, so we could get rid of 2-1-1, as that\'s the same.

To do this, we just divide by the number of ways we could arrange any given group of the size chosen. For this problem we could arrange three objects in 6 different ways (3 * 2 * 1),

=> we\'ll have to divide by 6, and get 36 different results.

Hence in 36 ways we could remove 3 pieces of candy from the bowl.