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1. 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?
(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
Solution:
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