A college delegation is made up of 6 basketball players, 5 volleyball players, 4 netball players, 3 badminton players and 2 tennis players. A subcommittee of four people is to be formed from these 20 athletes.

Find the probability that the subcommittee contains exactly one basketball player or exactly one volleyball player (or both).

My method:

let A be the event that committee has one basketball player

let B be event that committee has one volleyball player

so we want P (A U B)= P(A) + P(B) - P (A n B)

(n is intersect)

P(A) = 6C1 x 14C3/20C4

P(B) = 5C1 x 15C3/20C4

P(A n B) = 6C1 x 5C1 x9C2/20C4

my answer is 0.697 but the answer given is 0.414 can someone tell me where i went wrong? thanks~