On Halloween, a man presents a child with a bowl containing eight different pieces of candy. He tells her that she may have three pieces. How many choices does she have

choices

Step-by-step explanation:

We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy does not matter.

To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.

Anyways, back to the solving! Remember that the combination formula is

, where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.

In this case, and . Substituting these values into the formula gives us:

(Expand the factorials)

(Cancel out )

(Evaluate denominator)

(Cancel out )

Therefore, the child has different ways to pick the candies. Hope this helps!

the answer is here: : )

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