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
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
Why not 4c1*9c4