| 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? |
A) 6000
B) 6010
C) 6062
D) 6005
E) None of these
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 |
| \[={}^{9}{{C}_{5}}\times {}^{8}{{C}_{7}}+{}^{9}{{C}_{6}}\times {}^{8}{{C}_{6}}+{}^{9}{{C}_{7}}\times {}^{8}{{C}_{5}}\] |
| \[+{}^{9}{{C}_{8}}\times {}^{8}{{C}_{4}}+{}^{9}{{C}_{9}}\times {}^{8}{{C}_{3}}\] |
| \[=\,\,1008+2352+2016+630+56=6062\] |
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