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 in the committee. In how many ways can it be done? Choose the correct choice from the following answers:
A) 650	B) 656	C) 756	D) 760	E) 780
From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.   Hence we have the following 3 options.   We can select 5 men ...(option 1)   Number of ways to do this = 77565   We can select 4 men and 1 woman ...(option 2)   Number of ways to do this = 77564 × 67561   We can select 3 men and 2 women ...(option 3)   Number of ways to do this = 77563 × 67562   Total number of ways   = 77565 + (77564 × 67561) + (77563 × 67562)   = 77562 + (77563 × 67561) + (77563 × 67562)[∵ n756r = n756(n - r) ]   =   7   ×   6   2   ×   1   +   7   ×   6   ×   5   3   ×   2   ×   1   ×   6   =7×62×1+7×6×53×2×1×6   +   7   ×   6   ×   5   3   ×   2   ×   1   ×   6   ×   5   2   ×   1   +7×6×53×2×1×6×52×1   =   21   +   210   +   525   =756   756)
<result>C</result>
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 in the committee. In how many ways can it be done?