From a group of 7 women and 6 men, five persons are to be selected to form a committee so that at least 3 women are there in the committee. In how many ways can it be done? Choices
A) A)650
B) B)656
C) C)696
D) D)724
E) E)756
From a group of 7 women and 6 men, five persons are to be selected with at least 3 men.   Hence we have the following 3 options.   We can select 5 women ...(option 1)   Number of ways to do this = 7C5   We can select 4 men and 1 man ...(option 2)   Number of ways to do this = 7C4 × 6C1   We can select 3 women and 2 men ...(option 3)   Number of ways to do this = 7C3 × 6C2   Total number of ways   = 7C5 + (7C4 × 6C1) + (7C3 × 6C2)   = 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(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   =21+210+525= 
<gadget id="calculator">21+210+525</gadget>
<output>756</output>
756   756)
<result>E</result>
From a group of 7 women and 6 men, five persons are to be selected to form a committee so that at least 3 women are there in the committee. In how many ways can it be done?