How to Calculate a Number of Potential Outcomes


A permutation will tell you how many times an event can occur. This is a useful calculation when working with probability because probability requires that you know the total amount of possible outcomes and the total amount of favorable outcomes. In order to calculate a permutation, you need to know whether your outcome can have events repeat themselves. For example, in poker when you throw out a card, that card can not be played again, so it does not have repetition.

  • Determine the total number of possible outcomes on the first try. For example, assume you have a deck of cards. On the first try, you have 52 potential outcomes when you flip a card because there are 52 cards.

  • Determine whether there is replacement. Assume there is replacement with the cards.

  • Determine how many events will happen. In the example, assume you will flip the cards five times.

  • Multiply the number of outcomes on the first try by the number of outcomes on the first try minus one. Keep multiplying and subtracting one for as many times as the number of events that occurred. In the example, you have 52 cards that will be flipped five times. Subtract one from 52 to get 51. Subtract one from 51 to get 50. Continue subtracting one from the result two more times. Multiply 52 times 51 times 50 times 49 times 48, which equals 311,875,200 possible outcomes.

  • Raise the number of potential outcomes on the first event to the power of the total number of events to calculate the number of outcomes with replacement. "Raising to the power of," is another expression for saying you are using an exponent. In the example, you would raise 52 to the power of five, which equals 380,204,032 possible outcomes.


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