Question

My couch potato friend enjoys sitting in front of the TV and grabbing handfuls of 6 chocolates at random from his snack jar. Unbeknownst to him, I have replaced one of the 16 chocolates in his jar with a cashew. (He hates cashews with a passion.) How many possible outcomes are there the first time he grabs 6 chocolates?

Answer 1

There are 8008 possible outcomes are there the first time he grabs 6 chocolates

Explanation:

The order in which the chocolates are chosen is not important. So the combinations formula is used to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

How many possible outcomes are there the first time he grabs 6 chocolates?

6 chocolates from a set of 16. So

`C_(16,6) = (16!)/(6!(16 - 6)!) = 8008`

There are 8008 possible outcomes are there the first time he grabs 6 chocolates