11.1 Part 1 Permutations Worksheet
PC 12 Ch
Name: _____________________________
Date: __________________________
Block: ______
1. A student has 5 blouses, 4 skirts, and 4 sweaters. In how many different ways can she select an outfit
comprising 3 items?
2. Using the digits 1, 3, 5, 7, and 9, how many 3-digit whole numbers can be formed if there’s
a. No repetition
b. repetition is allowed
3.
A multiple-choice quiz has 8 questions, with 4 possible answers for each question. How many possible
ways are there to complete the test?
4.
A car license plate consists of 6 characters. Each character can be any of the letters from A to Z, or any
numeral from 0 to 9. How many license plates are possible?
5. A license plate can consist of UP TO 6 characters. Each character can be any letter from A to Z, or any
numeral from 0 to 9. How many license plates are possible?
6. The final score in a soccer game was 4 – 2. How many different scores are possible at half-time?
7. How many permutations are there of all the letters in each word?
a. Richmond
b. First
8. A model train has an engine, a caboose, a tank car, a flat car, a boxcar, a refrigerator car, and a stock
car. How many ways can all the cars be arranged between the engine and the caboose?
9.
There are 10 different books. How many ways can 4 of these books be arranged on a shelf?
10. Calculate the number of ways that an executive consisting of 4 people (president, vice president,
treasurer, and secretary) can be selected from a group of 20 people.
11. Evaluate each expression.
a.
8P2
b. 7P5
c. 6P6
d. 4P1
12. Show that 4!  3!  4  3!
13. What is the value of each expression?
a. 9!
b.
9!
5!4!
c. 5!3!
d. 64!
e.
102!
100!2!
f. 7!  5!
14. A combination lock has 60 numbers on it, from 0 to 59.
a. How many three-number combinations are possible?
b. How many three-number combinations are there that do not repeat any numbers in the
combination?
c. How many three-number combinations have at least two numbers the same?
15. How many ways can five students be seated at a round table?
16. In how many ways can fives students be seated at a round table if two students will not sit next to
each other?
17. Express each in the form of n Pr
a. 17 x 16 x 15 x 14 x13
b. 99 x 98 x 97 x 96
c. (n – 3) (n – 4) (n -5)
18. Use n Pn to show that 0! = 1
19. Change one letter at a time, creating a real word at each step, to change ONE into TWO. The best
solution requires the fewest steps.
ONE
_ __
_ __
.
.
.
TWO
Answers
1. 80
2a. 60
7a. 40,320 b. 120
12. On your own
b. 125 3. 65,536
8. 120 9. 5040
13a. 362,880
b. 126
14c. 10,680
16. 12
15. 24
17a. 17 P5
4. 2,176,782,336 5. 2, 238, 976, 116
6. 15
10. 116,280
11a. 56 b. 2,520 c. 720
d. 4
c. 720
d. 144 e. 5,151 f. 4,920 14a. 216,000 b. 205,320
b. 99 P4 c. n3 P3