A florist has 2 azaleas, 3 buttercups, and 5 petunias. The florist puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?  Choose the correct choice from the following answers
A) 31/45
B) 23/45
C) 14/45
D) 11/15
E) 8/15
The probability that two of the same flowers were chosen:   P(31/4531/45) = 2/10 * 1/9 = 2/90   P(BB) = 3/10 * 2/9 = 6/90   P(PP) = 5/10 * 4/9 = 20/90   The sum of these probabilities is 14/45   P(two flowers are different) = 1 - 14/45 = 31/45   The answer is 31/45.
<result>A</result>
A florist has 2 azaleas, 3 buttercups, and 5 petunias. The florist puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?