Committees by inclusion-exclusion

#IE#committees#at least one

Statement

From $7$ men and $5$ women, how many committees of $4$ contain at least one man?

Hint

Complement: committees with no man (all women).

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Total. $\binom{12}{4}=495$ .

No man. $\binom{5}{4}=5$ .

At least one man. $495-5=490$ .

Conclusion. $490$ committees.