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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 = 6^{4} = 1296

∴ 1296 four-digit numbers can be formed if repetition of digits is allowed.

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