NIMCET 2017 Question Paper with solutions

There are three number of ways by which we can form the committee.
(i) 3 Males and 2 Females
(ii) 4 Males and 1 Female
(iii) 5 Males + 0 Female Hence, total number of ways
= $\stackrel{7}{}{\mathit{C}}_8$ $\stackrel{6}{}{\mathit{C}}_2$ + $\stackrel{7}{}{\mathit{C}}_4\stackrel{6}{}{\mathit{C}}_2$ + $\stackrel{7}{}{\mathit{C}}_5\stackrel{6}{}{\mathit{C}}_0$
= $\frac{7\times 6\times 5}{3\times 2\times 1}$ × $\frac{6\times 5}{2\times 1}$ + $\frac{7\times 6\times 5}{3\times 2\times 1}$ × $\frac{6}{1}$ + $\frac{7\times 6}{2\times 1}$ × 1 = 525+ 210+ 21= 756
Hence, this can be done by 756 ways