Answers Permutation With Repetition Calculator

How many 7 digit PINs are possible?

This is permutation with repetition because the 7 PIN positions are ordered and each position can use any digit from 0 through 9, including repeats.

Exact result

10,000,000

10 choices for 7 ordered positions gives 10,000,000.

Each of the 7 PIN positions has 10 choices. PINs like 1234567 and 7654321 are different, and repeated digits like 0000000 are allowed, so the total is 10^7.

Worked steps

Show your work

  1. Inputs: n = 10, r = 7
  2. Formula: n^r
  3. Substitute: 10^7
  4. Steps: multiply 10 by itself 7 times
  5. Result: 10 choices for 7 ordered positions gives 10,000,000.

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Verify the same values in the calculator

Each of the 7 PIN positions has 10 choices. PINs like 1234567 and 7654321 are different, and repeated digits like 0000000 are allowed, so the total is 10^7.

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