a parent teacher committee consisting of 4 people is to be formed from 14 parents and 5 teachers. find the probability that the committee will consist of these people. assume that the selection will be random.
PART 1- 1 teacher and 3 parents
PART 2- All parents

Question

a parent teacher committee consisting of 4 people is to be formed from 14 parents and 5 teachers. find the probability that the committee will consist of these people. assume that the selection will be random. 
PART 1- 1 teacher and 3 parents
PART 2- All parents

anonymous · Answer

Opps I actually solved this earlier but I guess it lagged... Anyways :)

Hi! So we know that order doesn't matter. Thus we will be using C instead of P then.

So with the help of a calculator... (if you still don't understand it feel free to pm me and I'll help you along with this)...

We get, for PART 1, 5C1 * 14C3. Simply put, it means that we choose one teacher from 5, multiplied by choosing 3 parents from 14. So you can get this from punching in the numbers!

And for PART 2, we simply choose 4 parents from 14 parents. So, 14C4. I trust you can do that with the calculator...? :) It is actually 14*13*12*11/(4*3*2*1)

Hope that helped! Have a nice day! :)

kropot72 · Answer

$$P(3\ parents\ +\ 1\ teacher)=\frac{14C3\times 5C1}{19C4}$$
$$P(4\ parents)=\frac{14C4}{19C4}$$