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

Answer:

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

Step-by-step 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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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

6 chocolates from a set of 16. So

$C_{16,6} = \frac{16!}{6!(16 - 6)!} = 8008$

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