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From 6 men and 4 ladies a committee of 5 is...

This question belongs to Arithmetic Ability Permutation And Combination
Permutation and Combination
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From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?

Answer & Solution
Correct Answer: Option A
To committee can be formed in the following ways,
(1 lady + 4 gents) or (2 ladies + 3 gents) or (3 ladies + 2 gents) or (4 ladies + 1 gents) or (5 ladies + 0 gents).
Total number of possible arrangements,
= (4C1 × 6C4) + (4C2 × 6C3) + (4C3 × 6C2) + (4C4 × 6C1)
= 60 + 120 + 60 + 6
= 246
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2 Comments
Isha Singh
Isha Singh 6 years ago
At least one lady included in committee =Total no. of way in which committee can be formed - no lady included into committee
total no of way= 10C5
i.e 10C5 - 6C5
252-6 = 246
Hareem Shah
Hareem Shah 8 years ago
Why not 4c1*9c4
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