Permutation and combination(ALREADY SOLVED)

Question

Find the number of teams of 11 that can be selected from a group of 15 players if the youngest 2 players and at most one of the oldest two players are to be included

Ans:385

Answer 1

If I understand the question correctly...

You can partition your "set" of players into the different groups (youngest, "middle", oldest) which simplifies your problem. We have the...

2 youngest players

11 "middle aged" players

2 oldest players

Now you want 2 out of the 2 youngest players, 1 of the 2 oldest players, and thus 8 out of the 11 "other" players OR 2 out of the 2 youngest players, 0 of the 2 oldest players, and thus 9 out of the 11 "other" players.

The number of possible teams is then: $\binom{2}{2}\cdot\binom{2}{1}\cdot\binom{11}{8}+\binom{2}{2}\cdot\binom{2}{0}\cdot\binom{11}{9} = 1\cdot2\cdot165 +1\cdot1\cdot55=385$