There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?
A. 55
B. 60
C. 25
D. 192
Answer: Option B
Solution(By Examveda Team)
Since, no order to the committee is mentioned, a combination instead of a permutation is used. Let's sort out what we have and what we want. Have: 5 women, 6 men. Want: 3 women AND 1 man. The word AND means multiply. Woman and Men $$\eqalign{ & ^{{\text{have}}}{{\text{C}}_{{\text{want}}}}{ \times ^{{\text{have}}}}{{\text{C}}_{{\text{want}}}} \cr & { = ^5}{{\text{C}}_3}{ \times ^6}{{\text{C}}_1} \cr & = 60 \cr} $$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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