Question

Number of ways in which a committee of 6 persons can be formed out of 10 men and 5 women when at least one women is necessarily selected is

• A. $15P_{6} -^{10}P_{6}$
• B. $15C_{9} -^{10}C_{4}$
• C. $15C_{5} -^{10}C_{5}$
• D. None of these

Answer 1

Answer: (B)

$15C_{9} -^{10}C_{4}$

Answer 2

Number of ways without restriction = $15C_{6}$

Number of ways when no women is selected = $10C_{6}$

∴ Required ways

=$15C_{6} -^{10}C_{6} =^{15}C_{9} -^{10}C_{4}\mspace{6mu}\mspace{6mu}(\because^{n}C_{n - k} =^{n}C_{k})$