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propelledjeans

Member

Registered: 2010-01-22

Posts: 1

Discrete Mathematics

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?

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Re: Discrete Mathematics

a) 5! = 120

b)

c)

    However, this is true only if the committees are distinguishable from one another, if the committees are not distinguishable from one another then I think the answer needs to be divided by 3! or 6 since we can have the same groups of 4 people assinged to different committees, this gives

d)

    If we pick the chairpersons of the committees as a group of their own we end up with
   

    but this doesn't include all of the possibilities because you could make the chairpersons head different groups and this would be a different arrangement but it wouldn't be counted as a new arrangement under this total, so to take care of this we need to multiply this number by 5! or 120 and then we get

Lo and behold we get the same answer!
However, this is true only if the committees are distinguishable from one another, if the committees are not distinguishable from one another then I think the answer needs to be divided by 3! or 6 since we can have the same groups of 4 people assinged to different committees this gives

Last edited by Fruityloop (2010-01-23 04:34:29)