In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?
A. 266
B. 5040
C. 11760
D. 86400
E. None of these
Answer: Option C
Solution(By Examveda Team)
Required number of ways$$\eqalign{ & \left( {{}^8{C_5} \times {}^{10}{C_6}} \right) + \left( {{}^8{C_3} \times {}^{10}{C_4}} \right) \cr & = \frac{{8 \times 7 \times 6}}{{3!}} \times \frac{{10 \times 9 \times 8 \times 7}}{{4!}} \cr & = \frac{{8 \times 7 \times 6}}{{3 \times 2 \times 1}} \times \frac{{10 \times 9 \times 8 \times 7}}{{4 \times 3 \times 2 \times 1}} \cr & = 11760 \cr} $$
Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
Join The Discussion