A) 186
B) 168
C) 136
D) 169
E) None of these
Correct Answer: A
Solution :
Explanation Option (a) is correct. A committee of 5.persons, consisting of at most two ladies, can be formed n the following ways. (i) selecting 5 gents only out of 6. (ii) selecting 4 gents only out of 6 and one lady out of 4. (iii) selecting 3 gents only out of 6 and two ladies out of 4. In case I, the number of ways = \[^{6}{{C}_{5}}\] In case II, the number of ways =\[^{6}{{C}_{4}}{{\times }^{4}}{{C}_{2}}\] In case III, the number of ways = \[^{6}{{C}_{3}}{{\times }^{4}}{{C} _{2}}\] \[\therefore \] Required number of ways = \[^{6}{{C}_{5}}{{+}^{6}}{{C}_{4}}{{+}^{4}}{{C}_{1}}{{+}^{6}}{{C}_{3}}{{+}^{4}}{{C}_{2}}\] \[=\text{ }6+60+120=186\]
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