SOLUTION: A box contains 5 red, 4 blue and 3 white balls. In how many ways can we select 4 balls such that at least 2 are red?

Question 1023716: A box contains 5 red, 4 blue and 3 white balls. In how many ways can we select 4 balls such that at least 2 are red?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

There are 12C4 = 495 to select any 4 balls from the 12.

From that number, we must subtract  

1.  The number with no red balls:

That's 7C4 = 35 since there are 7 non-reds.

2.  The number with exactly 1 red ball.

We can choose the 1 red ball 5C1 = 5 ways.

For each of those 5 ways to choose the 1 red ball,
there are 7C3 = 35 ways to choose the other 3 balls.

That's 5*35 = 175

Final answer: 495 - 35 - 175 = 285 ways

Edwin

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