thesocialnetwork wrote:

A judo club has 10 members, of whom 2 are heavy weight players, 5 are middle weight players and 3 are light weight players. The club wants to send a team of 7 players to participate in a competition. The team must consist of a heavy weight player, 2 middle weight players, and 2 reserves from any weight category.

Find the number of ways in which the team can be selected.

My answer is simply 2C1 x 5C2 x 7C4 (remaining 4 players inclusive of reserves) = 420, but the answer given is 600. I'm not sure if it's something in the phrasing of the question i missed out, can anyone explain why? thanks!

Let's go by

**fam**'s interpretation.

If you have to name your reserves, then it is

On the other hand, if you don't have to name the reserves, then your team could have (heavy,middle,light) = (1,3,3), (2,2,3),(2,3,2), or (1,4,2). So there are

ways to name your team.