Permutation Worksheet

Permutation Worksheet

Permutation Worksheet

Name: ___________________________
Date: ___________________________
Class: ___________________________

A. Basic Permutation Questions

  1. Find the value of 5!5!.
  2. Find the value of 7!7!.
  3. Find the value of 8!8!.
  4. Find the value of 10!10!.
  5. Find 5P2^5P_2.
  6. Find 6P2^6P_2.
  7. Find 7P3^7P_3.
  8. Find 8P3^8P_3.
  9. Find 9P2^9P_2.
  10. Find 10P3^{10}P_3.

B. Use the Permutation Formula

Use:nPr=n!(n−r)!^nP_r=\frac{n!}{(n-r)!}

  1. Find 6P3^6P_3.
  2. Find 7P4^7P_4.
  3. Find 8P4^8P_4.
  4. Find 9P3^9P_3.
  5. Find 10P4^{10}P_4.
  6. Find 11P2^{11}P_2.
  7. Find 12P3^{12}P_3.
  8. Find 10P5^{10}P_5.
  9. Find 9P4^9P_4.
  10. Find 8P5^8P_5.

C. Multiple Choice

  1. How many ways can 3 students be arranged in a row?

a) 3
b) 6
c) 9
d) 12

  1. How many ways can 4 different books be arranged on a shelf?

a) 12
b) 16
c) 24
d) 36

  1. Which formula represents permutations of nn objects taken rr at a time?

a) n+rn+r
b) n−rn-r
c) n!(n−r)!\frac{n!}{(n-r)!}
d) n!r!\frac{n!}{r!}

  1. Find 5P3^5P_3.

a) 10
b) 20
c) 30
d) 60

  1. Find 6P4^6P_4.

a) 120
b) 240
c) 360
d) 720

  1. In permutations, does order matter?

a) Yes
b) No
c) Only sometimes
d) Never

  1. How many ways can 5 different people sit in a row?

a) 25
b) 60
c) 100
d) 120

  1. Find 7P2^7P_2.

a) 14
b) 21
c) 42
d) 49

  1. Find 8P2^8P_2.

a) 16
b) 32
c) 56
d) 64

  1. Find 9P3^9P_3.

a) 84
b) 252
c) 504
d) 729

D. Word Problems

  1. In how many ways can 4 different students stand in a line?
  2. In how many ways can 5 different books be arranged on a shelf?
  3. A class has 8 students. In how many ways can a president and vice-president be selected?
  4. There are 7 runners in a race. In how many ways can the gold, silver, and bronze positions be awarded?
  5. How many 3-letter arrangements can be made from the letters A, B, C, D, and E without repetition?
  6. How many 4-digit numbers can be formed using 1, 2, 3, 4, and 5 without repetition?
  7. A teacher has 6 different prizes. In how many ways can 3 prizes be awarded to 3 different students, with one prize per student?
  8. How many ways can 3 different paintings be selected and arranged from 6 paintings?
  9. A club has 10 members. In how many ways can a captain, vice-captain, and secretary be chosen?
  10. How many ways can 4 different people be chosen and arranged from a group of 7 people?

E. Permutations With Repeated Items

Use the formula:n!a!b!c!\frac{n!}{a!b!c!}

when some objects are identical.

  1. How many different arrangements can be made using the letters in MOM?
  2. How many different arrangements can be made using the letters in NOON?
  3. How many different arrangements can be made using the letters in LEVEL?
  4. How many different arrangements can be made using the letters in APPLE?
  5. How many different arrangements can be made using the letters in BANANA?

F. Challenge Questions

  1. How many ways can 6 people sit in a row?
  2. How many ways can 6 people sit in a row if two particular people must sit next to each other?
  3. How many 4-letter arrangements can be made from 7 different letters without repetition?
  4. How many ways can first, second, and third place be awarded among 12 contestants?
  5. A password consists of 4 different letters chosen from 8 letters. How many different passwords are possible?

Answer Key

A. Basic Permutations

  1. 120
  2. 5,040
  3. 40,320
  4. 3,628,800
  5. 20
  6. 30
  7. 210
  8. 336
  9. 72
  10. 720

B. Formula Practice

  1. 6P3=^6P_3 = 120
  2. 7P4=^7P_4 = 840
  3. 8P4=^8P_4 = 1,680
  4. 9P3=^9P_3 = 504
  5. 10P4=^{10}P_4 = 5,040
  6. 11P2=^{11}P_2 = 110
  7. 12P3=^{12}P_3 = 1,320
  8. 10P5=^{10}P_5 = 30,240
  9. 9P4=^9P_4 = 3,024
  10. 8P5=^8P_5 = 6,720

C. Multiple Choice

  1. b) 6
  2. c) 24
  3. c) n!/(n−r)!n!/(n-r)!
  4. b) 60
  5. b) 360
  6. a) Yes
  7. d) 120
  8. c) 42
  9. c) 56
  10. c) 504

D. Word Problems

  1. 24 ways
  2. 120 ways
  3. 56 ways
  4. 210 ways
  5. 60 ways
  6. 120 ways
  7. 120 ways
  8. 120 ways
  9. 720 ways
  10. 840 ways

E. Repeated Items

  1. 3 arrangements
  2. 6 arrangements
  3. 30 arrangements
  4. 60 arrangements
  5. 60 arrangements

F. Challenge Questions

  1. 720 ways
  2. 240 ways
  3. 840 ways
  4. 1,320 ways
  5. 1,680 ways