NCHMCT JEE 2015 Question Paper with solutions for online practice

We may have (1 man and 4 woman) or (2 man and 3 women) or (3 man and 2 women) or (5 women only)
∴ Required number of ways
= $\stackrel{6}{}{\mathit{C}}_1\times \stackrel{6}{}{\mathit{C}}_4+\stackrel{6}{}{\mathit{C}}_2$ × $\stackrel{6}{}{\mathit{C}}_3+\stackrel{6}{}{\mathit{C}}_3$ × $\stackrel{6}{}{\mathit{C}}_2+\stackrel{6}{}{\mathit{C}}_5$
= 6 × $\frac{6\times 5}{2}+\frac{6\times 5}{2}$ × $\frac{6\times 5\times 4}{3\times 2}$ + $\frac{6\times 5\times 4}{3\times 2}$ × $\frac{6\times 5}{2}$ + 6
= 90 + 300 + 300 + 6 = 696.