# When three dice are thrown what is the probbaility that all the three numbers are different.

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### 2 Answers

A die has 6 sides numbered from 1 to 6. In a fair die, each of the six numbers has an equal probability of turning up and the probability of any of the 6 numbers turning up is 1/6.

When the 3 dice are thrown there are 6*6*6 = 216 different permutations possible. The number of ways in which the three numbers can turn up different is 6*5*4 = 120. The probability of any event is equal to the number of outcomes favorable to the event divided by the total number of possible outcomes. The probability of the three numbers being different is `120/216 = 5/9`

**The required probability that the three numbers are different is **`5/9`

A die has 6 sides with each marked with a number from 1 to 6.

When 3 dice are thrown, the first one can turn up any number. If the second die should have a different number from that of the first, the probability of this happening is 5/6. If the third die should have a number different from the first 2, the probability of this happening is 4/6.

The product of 5/6 and 4/6 = 5/9.

The required probability is 5/9