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#1 Help Me ! » Discrete Mathematics » 2010-01-22 13:09:00

propelledjeans
Replies: 1

A small country has a parliament of 30 members. Each of the members is assigned to exactly one of 5 committees. Each committee has one chairperson. One of the committees requires 10 members, one requires 8 members, and the rest require 4.

(a) When the committees provide reports to the parliament, in how many ways may they be sequenced?
(b) Chairpersons are selected at random from the entire parliament. In how many ways may 5 chairpersons be selected from the members prior to being assigned to committees?
(c) In how many ways may the members be assigned to the committees, disregarding rank in the committee? (Chairpeople and normal members are not distinguished.)
(d) In how many ways can committees be formed if chairpersons are distinguished from the other members?

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