A chess club has 36 members. Members are categorized as Novice members, Regular members, and Master...

A chess club has 36 members. Members are categorized as Novice members, Regular members, and Master members. There are 8 Novice members, 21 Regular members, and 7 Master members in the club. For each part below, you must include a few words that describe your counting strategy. A number only as a response will not receive full credit.

(a) How many committees of size 5 can be chosen if the committee must have 1 Novice, 2 Regular, and 2 Master members?

(b) How many committees of size 5 can be chosen if the committee must have at most 2 Novice members?

(c) How many committees of size 5 can be chosen if the committee must have at least 1 Regular member and at least one Master member?

(d) How many committees of size 5 can be chosen if the committee must have at least 1 Regular member or at at least one Master member?

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