Question

Use counting arguments from the preceding chapter. My couch potato friend enjoys sitting in front of the TV and grabbing handfuls of 5 chocolates at random from his snack jar. Unbeknownst to him, I have replaced one of the 20 chocolates in his jar with a cashew. (He hates cashews with a passion.) How many possible outcomes are there the first time he grabs 5 chocolates?

Answer 1

Answer:

The total possible outcomes are 15,504.

Step-by-step explanation:

Consider the provided information.

My couch potato friend enjoys sitting in front of the TV and grabbing handfuls of 5 chocolates at random from his snack jar.

The jar has 20 items and we need to find the possible outcomes are there the first time he grabs 5 chocolates.

Here the sample space S is the set of 5 chocolates.

$n(S)=C(20,5)$

Therefore,

$C(20,5)=\frac{20!}{5!(20-5)!}$

$C(20,5)=\frac{20!}{5!15!}$

$C(20,5)=15504$

Hence, the total possible outcomes are 15,504.