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How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed? - Mathematics and Statistics

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Question

How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?

Sum
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Solution

Step 1: Choose the hundreds digit (first digit)

  • Cannot be 0.

  • From {1, 3, 5, 6} → 4 options

Step 2: Choose the tens digit (second digit)

  • One digit is already used in hundreds place.

  • Remaining digits = 4

  • But includes 0 (which is now allowed) → So 4 options

Step 3: Choose the units digit (third digit)

  • Two digits already used.

  • Remaining digits = 3 → So 3 options

Total numbers = 4 (choices for first) × 4 (second) × 3 (third)

= 48

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Permutations - Permutations When Repetitions Are Allowed
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Chapter 6: Permutations and Combinations - Exercise 6.1 [Page 73]

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Balbharati Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.1 | Q 5. (ii) | Page 73

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