Permutation with Repetition calculator

Permutation with repetition calculator calculates the total number of arrangements to select objects, where each object can be selected multiple times and the order of objects matters.

Permutation with Repetition calculator

Permutation with repetition formula is

ⁿP_r = n^r

where
n = number of objects
r = size of the selection (how many times of objects to be chosen)

Permutation with Repetition vs. Permutation without Repetition

  Permutation with Repetition Example

Permutation with repetition is commonly used in scenarios like setting a password.
For example, if you have a 6-digit passcode for your door lock, where each digit can be any number from 0 to 9.

For each digit in the passcode:

• The first digit has 10 options (0 through 9).
• The second digit also has 10 options.
• Repeats the third, forth one, fifth and sixth ones.

So, for a 6-digit passcode, you multiply the choices for each position:
10 x 10 x 10 x 10 x 10 x 10 = 10⁶ = 1,000,000

The calculation works because each digit in the passcode can be any of the 10 numbers (0-9), and this choice is repeated for each digit.

  Permutation Without Repetition Example

Using the example above, if you want to create a 6-digit passcode for your door lock where each digit is different, you would use a permutation without repetition.
This means that each digit in the passcode must be unique and can not repeat.

For each digits in the passcode:

• For the first digit, you have 10 choices (0-9).
• For the second digit, only 9 choices are left because one digit has already been used.
• For the third digit, 8 choices remain because two digits have been used.
• For the fourth digit, 7 choices remain.
• For the fifth digit, 6 choices remain.
• For the sixth digit, 5 choices remain.

Therefore, the total number of unique 6-digit passcodes without repetition is:
10 × 9 × 8 × 7 x 6 x 5 = 151,200

In summary, permutation with repetition allows for repeated use of digits, increasing the number of possible combinations compared to permutation without repetition.