Quantitative Aptitude Ques 2316
Question: A committee of 12 persons is to be formed from 9 women and 8 men. In how many ways this can be done if atleast 5 women have to be included in a committee?
Options:
A) 6000
B) 6010
C) 6062
D) 6005
E) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- Since, there are 9 women and 8 men. So, a committee of 12 consisting of atleast 5 women can be formed by choosing.
(i) 5 women and 7 men
(ii) 6 women and 6 men (iii) 7 women and 5 men (iv) 8 Women and 4 men (v) 9 women and 3 men
$ \therefore $ Total number of ways of forming the committee $ ={}^{9}C _5\times {}^{8}C _7+{}^{9}C _6\times {}^{8}C _6+{}^{9}C _7\times {}^{8}C _5 $ $ +{}^{9}C _8\times {}^{8}C _4+{}^{9}C _9\times {}^{8}C _3 $ $ =1008+2352+2016+630+56=6062 $
BETA
