Answer:
a) 78
b) 33
Explanation:
In order to have majority, the number of members is one party must be greater than the number of members in other party.
This means that one of the party must have at least 9 members.
a) Every party must have at least two members on the committee
[tex]\frac{(n+r-1)!}{r!} \\\frac{11+3-1}{11} \\=^{13}C_{11}\\= \frac{13 *12 *11!}{11! *2} \\= 13 *6\\= 78[/tex]
b) no group may have a majority of the committee members
Since , both the parties cannot have 9 members thus in order to compute the committee number in a way that no group may have a majority of the committee members
78 - ^{10} C_8
78-45
33
