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John has 12 marbles of different colors, including one red, one green, and one blue marble. In how many ways can he choose 4 marbles, if exactly one of the chosen marbles is red, green, or blue?

 Sep 9, 2018
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I assume you mean the other 9 marbles are some other color than red, green, and blue.

It matters if there are colors that are repeated.  I'll assume not.

 

I also assume that the order of the 4 chosen marbles doesn't matter.

 

We have to pick a red, green, or blue marble first.  There are 3 ways to do that.

 

We then have 3 marbles to choose for the 9 other marbles.  There are 9 choose 3 = 84 ways to choose these.

 

So there are 3 * 84 = 252 ways to choose marbles as specified

 Sep 9, 2018

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