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Say you have a playlist with 8 hiphop albums, 6 rock albums and 5 pop albums. You then want to create a new playlist with 3 albums from your other palylist.

How many ways are there that you can make your choice if

a) there is supposed to be one album from every genre?

My attempt: multiplication principle gives the answer: $8 * 6 * 5 = 240$ different ways.

b) all 3 albums are to be from the same genre?

My attempt: addition principle gives the answer: $8 + 6 + 5 = 19$ different ways.

Have I used the principles correctly?

Kaedos
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1 Answers1

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For (a), your solution is correct. There are $8 \choose 1$, $6 \choose 1$, and $5\choose 1$ ways to pick the albums in each genre. You were right to use the rule of product to multiply and to get $240$.

For (b), your solution is wrong. If you want all three albums from hiphop, there are $8 \choose 3$ ways to to do this. If you want all three from rock, you have $8 \choose 3$. Similar for pop.

So you get ${8 \choose 3} + {6 \choose 3} + {5 \choose 3} = 56 + 20 + 10 = 86$ ways. You were right about using the rule of sum, however.

Newb
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