1.A political discussion group consists of 8 Democrats and 15 Republicans.Seven people are selected to attend a conference.

a.In how many ways can seven people be selected from this group of twenty three?

b.In how many ways can seven Republicans be selected from the fifteen Republicans?

c.What is the probability that the group selected to attend the conference are all republicans?

2.The California lottery selects 5 numbered ping pong balls out of 50 ping pong balls.

a.How many possible outcomes are there?

b.To win the grand prize, a person has to correctly select 5 out of the 5 ping pong balls selected.What is the probability that they win the grand prize?

c.To win the second prize, a person has to correctly select 4 out of the 5 ping pong balls.What is the probability that they win the second prize?

d.If it costs $10 to play, the grand prize is $1,000,000, and the second prize is $50,000, what is the expected value of the lottery?