Permutation And Combination Ques 4
Question-
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can this be done?
(1) 564
(2) 645
(3) 735
(4) 756
(5) None of these
(SIDBI Officer Online Exam.24.02.2016)
Show Answer
Correct Answer: (4)
Solution: (4)
Number of committees =(3 men and 2 women) or ( 4 men and 1 woman) or (5 men) $={ }^{7} C_{3} \times{ }^{6} C_{2}+{ }^{7} C_{4} \times{ }^{6} C_{1}+{ } ^{7} C_{5} $ $=\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{6 \times 5}{2 \times 1}+{ }^{7} C_{3} \times 6+ { }^{7} C_{2} $
$\quad \quad\left[\because{ }^{n} C_{r}={ }^{n} C_{n-r}\right] $
$=525+\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times 6+\frac{7 \times 6}{2 \times 1} $ $=525+210+21=756$
BETA
