A committee of 5 members is to be formed by selecting out of 4 men and 5 women. In how many different ways… · ABC26GN5306

Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: Bank P.O. 2011

A committee of 5 members is to be formed by selecting out of 4 men and 5 women. In how many different ways the committee can be formed if it should have at least 1 man?
(a)115
(b)120
(c)125
(d)140
(e)None of these
Answer
Answer (as printed): C
Explanation
The committee should have (1 man, 4 women) or (2 men, 3 women) or (3 men, 2 women) or (4 men, 1 woman). Required number of ways = (4C1 × 5C4) + (4C2 × 5C3) + (4C3 × 5C2) + (4C6 × 5C1) = (4C1 × 5C1) + (4C2 × 5C2) + (4C1 × 5C2) + (4C4 × 5C1)  4 × 3 5 × 4  5 × 4 = (4 × 5) +  × + 4× + (1 × 5)  2 × 1 2 × 1   2 × 1  = (20 + 60 + 40 + 5) = 125.

Explanation as extracted from the printed page; notation may be imperfect.

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