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.