Probability Mixed Review
Directions: Show all work!
Name:__________________
1. A clothing store offers a lady’s sweater in 6 different colors, 5 different sizes, and 3 styles. How
many different ways can a sweater be purchased?
2. A bank requires customers to select a 4-digit PIN for their MAC card. The PIN can be any digit from
0 to 9 inclusive except the first digit may not be 0 or 9. How many different PIN’s can be formed?
3. How many different 6-place license plates can be formed if the first 2 places must be a letter and
the last 4 must be digits?
4. Evaluate:
7!
=
4!
5. Evaluate:
11!
=
6!5!
6. Evaluate:
8! 5!
=
4!
7. Evaluate:
P(7,3)
=
P(4,1)
8. How many ways can 4 books be placed on shelf from a selection of 10 different books if order doesn’t
matter?
9. How many different ways can a president, vice president, secretary, and treasurer be selected from a
group of 8 candidates?
10. How many different ways can 3 different algebra books, 2 different geometry books, and 2
different trigonometry books be arranged on a shelf?
11. How many distinguishable ways can 3 identical algebra books, 2 identical geometry books, and 2
identical trigonometry books be arranged on a shelf?
12. How many different ways can the letters in the word HANNAH be arranged?
Probability Mixed Review
13. How many different ways can the letters in the word FREEFORM be arranged if the two E’s must be
in the middle?
14. How many ways can 7 children form a circle for ring around the rosie?
15. How many ways can 10 charms be arranged on a bracelet that has no clasp if 4 charms are the same?
16. How many ways can 10 charms be arranged on a bracelet that has a clasp if 5 charms are the same?
17. Twelve toppings for pizza are available. In how many ways can a customer choose 3 toppings?
18. From a group of 8 Democrats and 6 Republicans, how many ways can a committee of 4 Democrats and
4 Republicans be formed?
19. The probability that Pat’s name will be drawn to win a door prize is 1 in 75. What are the odds that
Pat’s name will be drawn?
20. If the odds of snow on the day of a test is 1/9, what is the probability that it will snow on that day?
For questions 21-26 use the following: Mary brought a box of donuts to the office. The box contained 4
chocolate, 6 glazed, and 3 sugar-coated.
21. P(chocolate donut)=?
22. P(not sugar-coated)=?
23. P(vanilla)=?
Probability Mixed Review
24. P(2 glazed) without replacement=?
25. P(1 chocolate, 1 sugar-coated) without replacement?
26. P(glazed OR chocolate)=?
27. Abe, Betsy, and Charles are running for class president, and Doris, Ellen, and Frank are running for
vice president. How many possible president-vice-president combinations are possible?
28. List the sample space a rolling a 6-sided die then another 6 sided die (write out all possibilities)
29. Using the sample space in #33, what is the probability of rolling an even sum?
For questions #30-32, use the following: Suppose 3 families (Diazs, Kovars, and the Lippincotts) and are
lining up for a picture. Of those five families: there are 5 Diazs, 6 Kovars, and 3 Lippincotts.
30. How many different ways can they line up for a picture? Leave as a factorial.
31. How many different ways can they line up for a picture if the families must stick together? Do the
setup and leave as factorials.
32. How many different ways can they line up if the Diaz’s must be in the middle? Do the setup and leave
as factorials.
Probability Mixed Review
33. There are 4 men and 4 women. How many different ways can they circle up relative to a desk if
they must be alternating (one sex, then another)?
For questions #34-37 use the following: Six girls and eight boys are interested in an internship program
that can take 10 students.
34. How many ways can students be chosen for the internship?
35. How many ways can all the boys be selected and any 2 girls?
36. How many ways can the same number of girls and boys be selected?
37. What is the probability all of the boys will be selected?
Challenging (Extra Credit Type Problems):
1. Use the family setup in numbers 30-33. What is the probability that the families would line up like
#32 (where the families are together)?
2. How many ways in a 5-card hand from a standard deck of cards could I a draw a four of a kind (4
cards are the same, but different suits) and the fifth card can be anything? You must use combinations.