Applied Permutations Quiz � Real-Life Ordering Problems (HSS.CP.B.9)

1) A password consists of 5 unique letters chosen from 8. How many different passwords can be formed?

1680

6720

3360

5040

8P5 = 8 × 7 × 6 × 5 × 4 = 6720.

Explanation

8P5 = 8 × 7 × 6 × 5 × 4 = 6720.

2) How many permutations are there when choosing 4 books from a shelf of 7 to line up on a table?

420

840

210

5040

7P4 = 7 × 6 × 5 × 4 = 840.

Explanation

7P4 = 7 × 6 × 5 × 4 = 840.

3) How many 4-letter arrangements can be made from the letters in the word "MATH" without repetition?

8

12

24

16

There are 4P4 = 4! = 24 possible arrangements.

Explanation

There are 4P4 = 4! = 24 possible arrangements.

4) How many ways can the top 3 winners be chosen from 10 contestants if order matters?

720

120

210

60

10P3 = 10 × 9 × 8 = 720.

Explanation

10P3 = 10 × 9 × 8 = 720.

5) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if no digit repeats?

30

125

20

60

5P3 = 5 × 4 × 3 = 60.

Explanation

5P3 = 5 × 4 × 3 = 60.

6) How many different podium orders are possible for a 6-person race (gold, silver, bronze)?

90

120

60

36

6P3 = 6 × 5 × 4 = 120.

Explanation

6P3 = 6 × 5 × 4 = 120.

7) How many 2-letter “initials” can be made from the alphabet if letters cannot repeat?

702

676

600

650

26P2 = 26 × 25 = 650.

Explanation

26P2 = 26 × 25 = 650.

8) A code uses 2 distinct letters followed by 2 distinct digits (0–9). How many codes are possible?

25,000

52,000

40,000

58,500

26P2 = 26 × 25 = 650; 10P2 = 10 × 9 = 90; total 650 × 90 = 58,500.

Explanation

26P2 = 26 × 25 = 650; 10P2 = 10 × 9 = 90; total 650 × 90 = 58,500.

9) How many arrangements of 6 people are possible if they line up for a photo?

360

720

600

840

6P6 = 6! = 720.

Explanation

6P6 = 6! = 720.

10) How many ways can a president, vice president, and secretary be chosen from 8 people if no one holds more than one office?

336

210

56

168

8P3 = 8 × 7 × 6 = 336.

Explanation

8P3 = 8 × 7 × 6 = 336.

Applying Permutations in Context

1) A password consists of 5 unique letters chosen from 8. How many different passwords can be formed?

2)

What first name or nickname would you like us to use?

2) How many permutations are there when choosing 4 books from a shelf of 7 to line up on a table?

3) How many 4-letter arrangements can be made from the letters in the word "MATH" without repetition?

4) How many ways can the top 3 winners be chosen from 10 contestants if order matters?

5) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if no digit repeats?

6) How many different podium orders are possible for a 6-person race (gold, silver, bronze)?

7) How many 2-letter “initials” can be made from the alphabet if letters cannot repeat?

8) A code uses 2 distinct letters followed by 2 distinct digits (0–9). How many codes are possible?

9) How many arrangements of 6 people are possible if they line up for a photo?

10) How many ways can a president, vice president, and secretary be chosen from 8 people if no one holds more than one office?