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?

Darkside
Sep 9, 2018

#1**0 **

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

Rom
Sep 9, 2018