• # question_answer In how many ways can a committee be formed of 5 members from 6 men and 4 women if the committee has at least one woman [RPET 1987; IIT 1968; Pb. CET 2003] A) 186 B) 246 C) 252 D) None of these

The number of ways can be deduce as follows: 1 woman and 4 men ${{=}^{4}}{{C}_{1}}{{\times }^{6}}{{C}_{4}}=60$ 2 women and 3 men ${{=}^{4}}{{C}_{2}}{{\times }^{6}}{{C}_{3}}=120$ 3 women and 2 men ${{=}^{4}}{{C}_{3}}{{\times }^{6}}{{C}_{2}}=60$ 4 women and 1 man ${{=}^{4}}{{C}_{4}}{{\times }^{6}}{{C}_{1}}=6$ Required number of ways${{=}^{7}}{{C}_{4}}=35$.