SOLUTION: A bag contains 4 red, 6 white, and 9 blue marbles. How many ways can 5 marbles be selected if 2 are one color, and 3 are another?

Question 143038: A bag contains 4 red, 6 white, and 9 blue marbles. How many ways can 5 marbles be selected if 2 are one color, and 3 are another?
Found 2 solutions by stanbon, helpfulhint:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A bag contains 4 red, 6 white, and 9 blue marbles. How many ways can 5 marbles be selected if 2 are one color, and 3 are another?
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pick a color: 3 ways
pick 2 of that color: 4C2 + 6C2 + 9C2 = 6+15+36 = 57 ways
pick a different color: 2 ways
pick 3 of that color: 4C3 + 6C3 + 9C3 = 4+20+84 = 108
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Total # of ways:3*57*2*108 = 36936
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Cheers,
Stan H.
Answer by helpfulhint(1) (Show Source): You can put this solution on YOUR website!
Sorry Stan, but the answer was 2808 not 30,000+. Here is actually how to solve it:
First, I listed all the different possible combinations:
1. 2 red, 3 white
2. 2 white, 3 blue
3. 2 blue, 3 red
4. 2 red, 3 blue
5. 2 white, 3 red
6. 2 blue, 3 white
Then I put them into COMBINATION form:
1. 4C2 X 6C3 =120
2. 6C2 X 9C3 =1260
3. 9C2 X 4C3 =144
4. 4C2 X 9C3 =504
5. 6C2 X 4C3 =60
6. 9C2 X 6C3 =720
This is because you want to see how many different combinations you can have that meet the criteria.
Lastly, I added all the totals together:
120+1260+144+504+60+720=2808.
Your answer is 2808.
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