Applying Permutations in Context

  • 10th Grade
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| Attempts: 13 | Questions: 10 | Updated: Dec 10, 2025
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1) A password consists of 5 unique letters chosen from 8. How many different passwords can be formed?

Explanation

8P5 = 8 × 7 × 6 × 5 × 4 = 6720.

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About This Quiz
Applying Permutations In Context - Quiz

Permutations aren’t just math—they show up in real-world decisions, from seating charts to password codes. In this quiz, you’ll apply permutation formulas to solve contextual problems. Try this quiz to see how arrangement rules connect to everyday life.

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

Explanation

7P4 = 7 × 6 × 5 × 4 = 840.

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

Explanation

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

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

Explanation

10P3 = 10 × 9 × 8 = 720.

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

Explanation

5P3 = 5 × 4 × 3 = 60.

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

Explanation

6P3 = 6 × 5 × 4 = 120.

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

Explanation

26P2 = 26 × 25 = 650.

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

Explanation

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

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

Explanation

6P6 = 6! = 720.

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

Explanation

8P3 = 8 × 7 × 6 = 336.

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A password consists of 5 unique letters chosen from 8. How many...
How many permutations are there when choosing 4 books from a shelf of...
How many 4-letter arrangements can be made from the letters in the...
How many ways can the top 3 winners be chosen from 10 contestants if...
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5...
How many different podium orders are possible for a 6-person race...
How many 2-letter “initials” can be made from the alphabet if...
A code uses 2 distinct letters followed by 2 distinct digits (0–9)....
How many arrangements of 6 people are possible if they line up for a...
How many ways can a president, vice president, and secretary be chosen...
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