9.4-9.7 Review
Trig-Pre Calculus
Name: ________________________
Period:________ Date: ________
Verify each rule using Induction.
1. 13 + 23 + 33 + … + n3 =
𝑛2 (𝑛+1)2
4
Solve each of the following.
3. 8C3
4.
10C2
2. 1 + 4 + 7 + … + (3n – 2) =
5.
7P3
𝑛(3𝑛−1)
2
6.
10P2
Use the Binomial Theorem (or Pascal’s Triangle) to expand each of the following.
7. (x + 4)3
8. (x + 2y)4
9. (y – 2)5
Solve the following combinatorics/expected value problems.
10.
a) A race has 30 runners, how many different groups could make up the top 6 finishers?
b) If the top 6 finishers receive distinct trophies (1st place, 2nd place, etc.) How
many different ways could the race end?
11. Canada currently utilizes 37 distinct area codes. If the first digit of a 7 digit number
cannot be a 0 or 1, how many phone numbers does Canada have?
12. Current California License plate procedure uses the following format:
#-letter-letter- letter-#-#-#;
a) Calculate the total number of possible plate numbers for California.
b) Alabama follows #-#-#-#-letter-letter-#
c) Missouri follows letter-letter-#-letter-#-letter
13. The primary lottery in Canada, Lotto Max, consists of 7 numbers ranging from 1 to 49.
a) How many possible tickets are there?
b) Considering a max payout of $60 million Canadian Dollars ($45 million US),
what is the expected value of a ticket?
c) If it costs $5 to play, is the game fair?
14. You draw one card from a standard deck of playing cards. If you pick a heart, you will
win $10. If you pick a face card, which is not a heart, you win $8. If you pick any other
card, you lose $6. Do you want to play? Explain.
15. The world famous gambler from Philadelphia, Señor Rick, proposes the following game of
chance. You roll a fair die. If you roll a 1, then Señor Rick pays you $25. If you roll a 2,
Señor Rick pays you $5. If you roll a 3, you win nothing. If you roll a 4 or a 5, you must
pay Señor Rick $10, and if you roll a 6, you must pay Señor Rick $15. Is Señor Rick loco
for proposing such a game? Explain.