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?

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FelisFelis FelisFelis · Answer 1 · 2019-11-05T07:24:33+01:00

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.

[tex]n(S)=C(20,5)[/tex]

Therefore,

[tex]C(20,5)=\frac{20!}{5!(20-5)!}[/tex]

[tex]C(20,5)=\frac{20!}{5!15!}[/tex]

[tex]C(20,5)=15504[/tex]

Hence, the total possible outcomes are 15,504.