Question: A florist has 2 Azaleas, 3 Buttercups, and 4 Petunias. She put two flowers together at random in a bouquet. However a customer does not want two of the same flower. What is the probability that the florist does not have to change the bouquet ?

I tried answering the above problem in two ways.

1) Prob of having 1 azalea&1 buttercup in a bouquet OR 1 buttercup&1 petunia in a bouque OR 1 Petunia&1 azalea in a bouquet.

=> 2/9*3/8 + 3/9*4/8 + 4/9*2/8 = 26/72

2) 1 - (Prob of having 1 azalea&1azalea OR 1 buttercup&1 buttercup OR 1petunia&1 petunia)

=> 1 - (2/9*1/8 + 3/9*2/8 + 4/9*3/8) = 1 - 20/72 = 13/18

My question is why am I getting TWO different answers. They both have to be the same. 13/18 is the correct answer, as per the Guide. What is the mistake I 'm doing in my FIRST approach