### Instruction: A bin has 8 black balls and 7 white balls.  3 of the balls are drawn at random.  What is the probability of drawing 2 of one color and 1 of the other color?### Response: Ok, so the probability of drawing 2 black balls and 1 white ball is the number of ways to draw 2 black balls and 1 white ball divided by the total number of ways to draw 3 balls.
Right, so the number of ways to draw 2 black balls and 1 white ball is 8 choose 2 times 7 choose 1.
That's correct, which is equal to 28*7 = 196.
And the total number of ways to draw 3 balls is 15 choose 3, which is equal to 455.
So the probability of drawing 2 black balls and 1 white ball is 196/455.
Right, but we can also draw 2 white balls and 1 black ball.
Oh, that's right. The probability of drawing 2 white balls and 1 black ball is the number of ways to draw 2 white balls and 1 black ball divided by the total number of ways to draw 3 balls.
Right, so the number of ways to draw 2 white balls and 1 black ball is 7 choose 2 times 8 choose 1.
That's correct, which is equal to 21*8 = 168.
And the total number of ways to draw 3 balls is 15 choose 3, which is equal to 455.
So the probability of drawing 2 white balls and 1 black ball is 168/455.
So the probability of drawing 2 of one color and 1 of the other color is 196/455 + 168/455 which is equal to 364/455.