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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?

A. 246

B. 340

C. 290

D. 315

Answer: Option A

Solution(By Examveda Team)

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

This Question Belongs to Arithmetic Ability >> Permutation And Combination

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Comments ( 2 )

  1. Isha Singh
    Isha Singh :
    4 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

  2. Hareem Shah
    Hareem Shah :
    6 years ago

    Why not 4c1*9c4

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