I'm learning Permutations and Combinations and while trying to solve this simple question, I stuck on the solution:-
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
The solution was to consider all three possibilities one by one- 3 men and 2 women, 4 men and 1 women, all 5 men. Calculate the combinations for each case and add them.
But I was trying it from a different approach- Firstly select 3 men from 7 (gives 35 combinations) and multiply it with the combinations of selecting 2 more committee members from 10 remaining members. So my answer came out to be 35 x 45 = 1575. But the answer is 756 which is not even a multiple of 35. So is my approach wrong? Why so?