Problem Solving

Mr.Hollywood wrote:A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts two flowers together at random in a bouquet. But the customer doesn't want two of the same flower in one bouquet. What is the probability that the florist does not have to change the bouquet?

Thanks guys!

Probability that the florist does not have to change the bouquet = 1 - (probability that the two flowers are azaleas + probability that the two flowers are buttercups + probability that the two flowers are petunias)
= 1 - [(2/9 * 1/8) + (3/9 * 2/8) + (4/9 * 3/8)]
= 1 - [20/72]
= 1 - 5/18
= [spoiler]13/18[/spoiler]