SOLUTION: A box contains 7 white balls and 6 red balls. If Van chooses 9 balls at random from the box, what is the probability that he will select 4 white balls and 5 red balls? I had tr

Question 1020101: A box contains 7 white balls and 6 red balls. If Van chooses 9 balls at random from the box, what is the probability that he will select 4 white balls and 5 red balls?
I had tried 7/9 X 6/8 , 4/7 X 5/6. Also tried (7/9)^2 X (6/8)^2....the answer is supposed to be .294, but I can't get that. Thanks
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
You are randomly guessing. Please review the nCr operator (the binomial coefficient, i.e. n choose r). Otherwise you will be lost in this solution.

Here, we will assume the balls are distinguishable. How many ways can you choose 9 balls from a box containing 13 balls? The number of such ways is 13C9 ("13 choose 9") = 13!/9!*4! = 715.

Now you want the number of ways Van can choose exactly 4 white and 5 red balls. The number of ways is 7C4 * 6C5 = 35*6 = 210.

The probability is 210/715 = 0.2937...
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