Question

Andy has to join 2 clubs in his school. The clubs are divided into 3 categories: 5 in art, 4 in sports, and 5 in sciences.

How many ways can Andy join 2 clubs from different categories?
What's the probability of choosing 2 clubs from the same category?

Answer 1

total clubs are 5+4+5=14
Number of ways he can choose clubs are 14*13= 182
Number of ways he can choose clubs from same category=sum of number of ways he can select clubs from each category=5*4 + 5*4 + 4*3=20+20+12=52

Now P(E)=52/182=26/91

Answer 2

You need to know the concepts of Permutation and Combinations to solve this problem