13A family has 5 children Assume that each child is as likel

13.A family has 5 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 5 girls if it is known the family has at least one girl.

15. You own 22 CDs. You want to randomly arrange 7 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?

17. There are 364 students in a college who have taken a course in calculus, 211 who have take a course in discrete mathematics, and 160 who have taken a course in both calculus and discrete mathematics. How many students at this college have taken a course in either calculus or discrete mathematics?

19. 15 players for a softball team show up for a game:
(a) How many ways are there to choose 10 players to take the field?
(b) How many ways are there to assign the 10 positions by selecting players from the 15 people who show up?
(c) Of the 15 people who show up, 5 are women. How many ways are there to choose 10 players to take the field if at least one of these players must be women?

Solution

15)

There are 22 P 7 = 22!/(22-7)! = 22!/15! =859541760 different ways to arrange 22 CDs into 7 positions


However, there is only one way to get them into alphabetical order (assuming each CD has a unique name)


So the probability that the rack ends up in alphabetical order is 1/859541760