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Each of five, standard, six-sided dice is rolled once. What is the probability that there is at least one pair?  (In other words, what is the probability that there are two rolls that are equal?)

 Feb 6, 2022
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Since there are 5 dice, there are 65 = 7776 possible outcomes.

To find the number of ways that there will be at least one pair, find the number of ways that there are

no pairs and subtract this from the number of possible outcomes.

To have no pairs: there are 6 possibilities for the first die, 5 possibilities for the second die,

4 possibilities for the third die, 3 possibilities for the fourth die and 2 possibilities for the fifth die.

Multiplying these together, there is a total of 720 possibilities that there will be no pair.

7776 - 720 = 7056 ways to have at least one pair.

The probability is:  7056 / 7776.

 Feb 7, 2022

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