MATH 222 FALL 2011, Assignment Two
(Answer Key)
1. A 30member mathematics department must select one person to chair the discrete
mathematics committee and two other people to cochair the calculus committee.
(a) In how many ways can this be done?
The procedure consists of selecting a member to chair the discrete math committee
(
30
1
ways), followed by selecting two other members to cochair the calculus com
mittee (
29
2
ways). By the rule of product, there are
30
1
29
2
ways to complete the
entire procedure.
(b) In how many ways can this be done if Professor Blue refuses to chair the discrete
mathematics committee?
Following the setting in (a), the two selections can be performed respectively in
29
1
and
29
2
ways. Thus, there are
29
1
29
2
ways to complete the procedure.
(c) In how many ways can this be done if Professor Green refuses to cochair the
calculus committee?
In this case, we select two members to cochair the calculus committee (
29
2
ways),
followed by selecting a member to chair the discrete mathematics committee (
28
1
ways). There are
29
2
28
1
ways.
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 Spring '11
 HuangJing
 Calculus, Combinatorics, ways, Professor Green, cochair

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