Simple Probability Question: Show work please! 20 politicians are having a tea p

Question

Simple Probability Question: Show work please!

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?

Explanation / Answer

(a) Different ways to choose people perform tasks =20C317C215C6 = 20!/ (9! 3!2! 6!) = 775, 975, 200

First 3 person who set table can be chosen from 20 people and rest 2 people can be chosen from 17 and out of rest of 15 people, we can choose the rest of 6.

(b) Total possibilites : Here all Democrats hate tea. Tea was given only to 10 out of 20 people. so we have to find out that only Republicans were serve Tea. so 10 tea only be delivered to republicans only.

so Probability = 14C10 / 20C10 = 1001/ 184756 = 0.0054

(c) Probability that tea will be served to 9 Republicans and 1 Democrat

Probability = 14C9 * 6C1/ 20C10  = 2002 * 6/ 184756 = 0.065

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