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How to Calculate Possible Permutations

Permutations is a mathematical way to tell you how many different possibilities exist that something can happen. With permutations, the order of numbers does matter. The easiest way to think of a permutation is with a lock. You can enter the right numbers, but if they are in the wrong order, then it will not work. There are two types of permutations, those with repetition of outcomes or ones without repetition of outcomes.

Instructions

  1. With Repetition

    • 1

      Write out the different possibilities that can occur. For example, assume you have dice, so your outcomes a 1, 2, 3, 4, 5 and 6. Dice would provide an example of repetition because you can roll the same number more than once.

    • 2

      Count up the number of outcomes you have. In the example, you have six.

    • 3

      Determine the number of times an outcome can occur. In the example, assume you will roll the die three times.

    • 4

      Raise the different outcomes you have to the power of the number of times the outcome can occur. In the example, six raised to the third power equals 216 different outcomes.

    Without Repetition

    • 5

      Determine the number of possible outcomes you have. For example, assume you have a deck of cards and are not going to put the card back in the deck once it is drawn. You have 52 possible outcomes.

    • 6

      Determine the number of times you will let an outcome occur. In the example, assume you will pick four cards.

    • 7

      Multiply the number of possible outcomes by one less than the number of possible outcomes. Keep multiplying and subtracting one until you multiply the numbers the amount of times you will let the outcome occur. In the example, 52 times 51 times 50 times 49 equals 6,497,400 possible results.

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