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How many committees of $5$ can be chosen from $10$ people if each committee includes Alice and excludes Bob?

How many committees of $5$ can be chosen from $12$ people if each committee

(i) includes Alice;

(ii) excludes Bob;

(iii) includes Alice and excludes Bob;

(iv) includes at least one of either Alice or Bob

Please help answers this problem and include the explanation of how to get the answers. Thanks you.

2 Answers 2