Math
posted by Brandi on .
Need help on how to solve this problem..
Five cards are chosen from a deck of playing cards and put into a pile. Three of the cards are red and 2 of the cards are black. A second pile is made using 2 red cards and b black cards. One card from each pile is chosen randomly. The probability of choosing a red card from each of the piles is 6/45. How many black cards, b , are in the second pile? The answer is 7 but I don't know why that is the answer. Thanks...

call the 2 piles x and y
P(x) = 3/5
P(y) = 2/(b+2)
3/5 * 2/(b+2) = 6/45
6 / 5(b+2) = 6/45
5(b+2) = 45
b+2 = 9
b = 7