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?

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



[ From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if there is no restriction about its formation?
Solution:
From 6 men and 4 ladies, a committee of 5 is to be formed.
Total number of possible arrangements, if there is no restriction about its formation
= ^{(6 + 4)}C₅
= ¹⁰C₅
= 252 ]