Use counting arguments from the preceding chapter My couch p

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 16chocolates in his jar with a cashew. (He hates cashews with a passion.)

A.) How many possible outcomes are there the first time he grabs 5 chocolates?
4368 outcomes

B.) How many of these include the cashew??

I did part A just need help with part B please.

Solution

[as mentioned in the question only part B is answered]

B)

now out of the 5 chocolates that he grabs there are two possiblities

1. all 5 are chocolates

2. 4 are chocolates and 1 cashew.

so the cashew is included only if he grabs 4 chocolates from 15 chocolates and 1 cashew from 1 cashew

which can be done in ¹⁵C₄*¹C₁=1365 ways.

so out of 4368 outcomes 1365 outcomes include the cashew. [answer]