Out of 5 women and 4 men, a committee of three members is to be formed in such a way that at least one member is a women. In how many different ways can it be done ?
A. 76
B. 80
C. 84
D. 96
E. None of these
Answer: Option B
Solution(By Examveda Team)
Required number of ways$$\left( {{}^5{{\text{C}}_1} \times {}^4{{\text{C}}_2}} \right) + \left( {{}^5{{\text{C}}_2} \times {}^4{{\text{C}}_1}} \right)$$ $$ + \left( {{}^5{{\text{C}}_3}} \right)$$
$$ = \left( {5 \times \frac{{4 \times 3}}{{2 \times 1}}} \right)$$ $$ + \left( {\frac{{5 \times 4}}{{2 \times 1}} \times 4} \right)$$ $$ + \left( {\frac{{5 \times 4 \times 3}}{{3 \times 2 \times 1}}} \right)$$
$$\eqalign{ & = \left( {30 + 40 + 10} \right) \cr & = 80 \cr} $$
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!
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