Find the number of 4-digit numbers that can be formed using the digits 1, 2, 4, 5, 6, 8 if digits can be repeated. - Mathematics and Statistics

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Sum

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 4, 5, 6, 8 if digits can be repeated.

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Solution

A 4-digit number is to be made from the digits 1, 2, 4, 5, 6, 8 such that digits can be repeated.
∴ Unit’s place digit can be filled in 6 ways.
10’s place digit can be filled in 6 ways.
100’s place digit can be filled in 6 ways.
1000’s place digit can be filled in 6 ways.
∴ total number of numbers = 6 × 6 × 6 × 6 = 64 = 1296
∴ 1296 four-digit numbers can be formed if repetition of digits is allowed.

Concept: Permutations - Permutations When Repetitions Are Allowed
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Chapter 6: Permutations and Combinations - Exercise 6.3 [Page 81]

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Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.3 | Q 10. (i) | Page 81

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