1) A committee of five is going to be selected from a
group of twenty people.
a) How many different committees are possible if there is no
distinction between the responsibilities of the five members?
b) How many different committees are possible if one person is
the chair, and the rest are general members?
2) In Florida, juries for certain types of trials are
made up of 6 people, and the decision must be unanimous.Suppose a
jury pool consists of 17 people. In today’s jury pool, there are 10
men and 7 women.
a) How many different groups of 6 are there, not taking gender
into account?
b) How many ways are there to select 6 men from the group of 10
men?
c) Compute the probability that a randomly selected jury of 6
people is made up of only men. Write your answer as a percent,
rounded to the nearest tenth of a percent.
3) In the lottery game called 5/21, a player picks five
numbers from 1 to 21.
a) If all five of the numbers match the ones that are drawn, the
player wins first prize. What is the probability of winning this
prize? Enter your answer as a decimal (not a percent), rounded to
five decimal places.
b) If four of the five numbers match the ones that are drawn,
but the other number doesn’t match, the player wins second prize.
What is the probability of winning this prize? Enter your answer as
a decimal (not a percent), rounded to five decimal places.
c) If three of the five numbers match the ones that are drawn,
but the other two numbers don’t match, the player wins third prize.
What is the probability of winning this prize? Enter your answer as
a decimal (not a percent), rounded to five decimal places.
