Answers Permutation With Repetition Calculator

How many 10 digit PINs are possible?

This is permutation with repetition because the 10 PIN positions are ordered and each position can use any digit from 0 through 9, including repeats.

Exact result

10,000,000,000

10 choices for 10 ordered positions gives 10,000,000,000.

Each of the 10 PIN positions has 10 choices. PINs like 1234567890 and 0987654321 are different, and repeated digits like 0000000000 are allowed, so the total is 10^10.

Worked steps

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

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Each of the 10 PIN positions has 10 choices. PINs like 1234567890 and 0987654321 are different, and repeated digits like 0000000000 are allowed, so the total is 10^10.

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