Question

2. 20 politicians are having a tea party, 6 Democrats and 14 Republicans. To prepare, they need to choose: 3 people to set the table, 2 people to boil the water, 6 people to make the scones. Each person can only do 1 task. (Note that this doesn’t add up to 20. The rest of the people don’t help.)

(a) In how many different ways can they choose which people perform these tasks?

(b) Suppose that the Democrats all hate tea. If they only give tea to 10 of the 20 people, what is the probability that they only give tea to Republicans?

(c) If they only give tea to 10 of the 20 people, what is the probability that they give tea to 9 Republicans and 1 Democrat?

I don't get this at all thanks!!

Answer 1

a) Number of different ways to choose here could be computed as:

= Number of ways to choose 11 out of the 20 politicians * Number of ways to choose 3 out of those 11 selected who would set the table * Number of ways to choose 2 people out of the 8 people who would boil

b) Probability that the only give tea to republicans is computed here as:

= Number of ways to select 10 people who get tea out of the 14 republicans / Total number of ways to select 10 people out of the 20 people

Therefore 0.0054 is the required probability here.

c) Probability that they give tea to 9 Republicans and 1 Democrat is computed as:

Therefore 0.0650 is the required probability here.