Permutation And Combination Ques 9
Question-
From a group of 7 men and 6 women five persons are to be selected to form a committee such that at least 3 men are there on the committee. In how many ways can the committee be formed?
(1) 756
(2) 765
(3) 860
(4) 654
(5) 760
(Indian Bank Specialist Officer SO Exam, 08.03.2020)
Show Answer
Correct Answer: (1)
Solution: (1)
Cases of combination: I. 3 men and 2 women
II. 4 men and 1 woman
III. 5 men
$\therefore$ Total number of ways of selection
$ \begin{aligned} &={ }^{7} C_{3} \times{ }^{6} C_{2}+{ }^{7} C_{4} \times{ }^{6} C_{1}+{ }^{7} C_{5} \\ &={ }^{7} C_{3} \times{ }^{6} C_{2}+{ }^{7} C_{3} \times{ }^{6} C_{1}+{ }^{7} C_{2} \\ & {\left[\because{ }^{n} C_{r}={ }^{n} C_{n-r}\right] } \\ &=\frac{7 \times 6 \times 5}{1 \times 2 \times 3} \times \frac{6 \times 5}{1 \times 2}+\frac{7 \times 6 \times 5}{1 \times 2 \times 3} \times 6+\frac{7 \times 6}{1 \times 2} \\ &=35 \times 15+35 \times 6+21 \\ &=525+210+21 \\ &=756 \end{aligned} $
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