A sub-committee of 3 people must be chosen from a group of 9 teachers (which includes the principal). How many sub-committees may be chosen:

a)that contain the principal?

b) that do not contain the principal?

Question

A sub-committee of 3 people must be chosen from a group of 9 teachers (which includes the principal). How many sub-committees may be chosen:

a)that contain the principal?

b) that do not contain the principal?

ganpat · Answer

a) 9C3... as it includes Principle and Principle is included in group of teachers..

anonymous · Answer

that is what I got as well but the answer says 28??

ganeshie8 · Answer

a) 8C2

ganeshie8 · Answer

you fix the principal.
next 2 ppl you chose from 8 ppl

ganeshie8 · Answer

b) 8C3

ganeshie8 · Answer

you remove the principal from your 9 choices - 
you're left with 8 choices 

you need to pick 3 ppl from 8

anonymous · Answer

yep but why isn't it 9C3?

anonymous · Answer

for part a

ganpat · Answer

@ganeshie8 : hmmm, u r right...

ganeshie8 · Answer

in 9C3

some combinations WILL NOT have principal

ganeshie8 · Answer

so you fix the principal, 
and FILL remaining two places by choosing from remaining 8 ppl

anonymous · Answer

oh kk, I get it now.

ganeshie8 · Answer

okiee :)