6.

a) How many ways are there to select 5 students from a class of 30to serve on a committee?

b) How many ways are there to select 5students from a class of 30to hold five different executive positions on a committee?

c) How many bit strings of length 16have equal numbers of 0's and 1's?

7.

(a) What is the probability that a card chosen from an ordinary deck of 52 cards is a queen?

(b) What is the probability that a fair coin lands Heads exactly 3times out of 4flips?

8.

Suppose you have a class with 30 students 10 freshmen, 12 sophomores, and 8 juniors.

a) You pick three students at random, one at a time. What is the probability that all three are junior?

b) You pick two students at random, one at a time. What is the probability that the second student is a sophomore, given that the first is a freshman?