# Math Help - Combinatorial probability question

1. ## Combinatorial probability question

im sure this will be easy for most, i just am having trouble knowing where to start as im new to probability. the question is as follows:

"A science committee of 3 people is to be formed from a group of 17 scientists (7 biologists, 4
physicists and 6 chemists) with each possible committee equally likely.
What is the probability the committee vote in favour of a proposal given:

(a) all biologists in favour, everybody else against?
(b) all chemists against, everybody else in favour?
(c) all biologists in favour, all chemists against and all physicists abstain?"

thanks

2. In order to do this we must assume that a proposal passes on simple majority vote: 2 to 1 or 3 to 0.
To do part (a) then we must have two biologists and one other or all three biologists.
What is the probability of each of those committees?

3. Originally Posted by Plato
In order to do this we must assume that a proposal passes on simple majority vote: 2 to 1 or 3 to 0.
To do part (a) then we must have two biologists and one other or all three biologists.
What is the probability of each of those committees?
7 choose 2 times by 10 choose 1??

$\displaystyle\frac{\binom{7}{2}\binom{10}{1}}{\bin om{17}{3}}+\frac{\binom{7}{3}\binom{10}{0}}{\binom {17}{3}}$.