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
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.