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Answers Permutation With Repetition Calculator

How many 5 digit PINs are possible?

This is permutation with repetition because the 5 PIN positions are ordered and each position can use any digit from 0 through 9, including repeats.

Exact result

100,000

10 choices for 5 ordered positions gives 100,000.

Each of the 5 PIN positions has 10 choices. PINs like 12345 and 54321 are different, and repeated digits like 00000 are allowed, so the total is 10^5.

Worked steps

Show your work

  1. Inputs: n = 10, r = 5
  2. Formula: n^r
  3. Substitute: 10^5
  4. Steps: multiply 10 by itself 5 times
  5. Result: 10 choices for 5 ordered positions gives 100,000.

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Each of the 5 PIN positions has 10 choices. PINs like 12345 and 54321 are different, and repeated digits like 00000 are allowed, so the total is 10^5.

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