Probabaility of having certain number of parents in a committee

[desmond iking]

Homework Statement

A committee of 5 members is formed from 6 parents , 2 teachers, and a principal, In how many ways, can this committee be formed if the committee consists of not more than 4 parents?

my working is 1 parent + 2 parents + 3 parents +4 parents

which is (6C1 x 8C4) + (6C2 x 7C3) +(6C3x 6C2)+ (6C4 x 5C1)

but the ans given is only 120

Homework Equations

The Attempt at a Solution

 

[LCKurtz]

Homework Statement

A committee of 5 members is formed from 6 parents , 2 teachers, and a principal, In how many ways, can this committee be formed if the committee consists of not more than 4 parents?

my working is 1 parent + 2 parents + 3 parents +4 parents

which is (6C1 x 8C4) + (6C2 x 7C3) +(6C3x 6C2)+ (6C4 x 5C1)

but the ans given is only 120

Homework Equations

The Attempt at a Solution

Since there are only 3 non-parents your choices for number of parents are 2,3, and 4. Once you have counted the parents, the others must be chosen from the non-parents. Try again.

 

[Ray Vickson]

Since there are only 3 non-parents your choices for number of parents are 2,3, and 4. Once you have counted the parents, the others must be chosen from the non-parents. Try again.

Does the identities of the parents and teachers matter? In other words, would a 3-parent committee having parents Smith, Jones and Chakravarty be counted separately from a 3-parent committee having parents Smith, Jones and Salam? Ditto for the teachers.