**1. The problem statement, all variables and given/known data**

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?

**2. Relevant equations**

none

**3. The attempt at a solution**

Favour =Majority of comitte favour i.e at least 2 of 3 favour

__For question 1__

Sample space = (17C3)=680

If biologist all favour.. Then for favour, 2 biologist or 3 biologist in the comitee

Event 1= 2 biologist and 1 other=(7C2)*(10C1) =210

Event 2= 3 biologist and 0 other=(7C2)*(10C0) =35

245/Sample space = 245/680 = 49/136=36%

IS THIS CORRECT???

__For question 2__

Sample space = (17C3)=680

If bioligist all favour + phyicists all favour + all chemist against. Then we have many events. So is better to use addition rule.

Addition rule = E + NOT E=Sample Space..............where E= favour

NOT E= 2 chemists or 3 chemists in comitee

Event 1= 2 chemist and 1 other=(6C2)*(10C1) =150

Event 2= 3 chemist and 0 other=(6C2)*(10C0) =15

NOT E=150+15=165

(Sample space-NOT E) = E=680-165=515

515/Sample Space=Probability of E=515/680=103/136=75.7%

IS THIS CORRECT METHOD???

__For question 3__

Sample space = (17C3)=680

If all biologist favour + all chemist against + all physicists dont give a damn.

Favour = (3 biologist)+(2 biologist+1 Other) =Question 1

Favour = (1 bioligist + 2 physicists) +(2 bioligist + 1 physicists)

Favour = (2 bioligist + 1 chemist)

Then we have many events. So is better to use addition rule.

NOT favour=(1 chemist + 2 physicist) + (2 chemist + 1 physicist) + (3 chemist)

NOT favour=(2 chemist + bioligist)

NOT favour=(6C1)(4C2) + (6C2)(4C1) +(6C3) + (6C2)(7C1)=36+60+20+105=221

Sample space - NOT favour = 680-221=459

459/680=27/40=67.5%

IS THIS CORRECT METHOD AND ANSWER???