Suppose you had 5 regular dice. What are the odds of rolling a 2, 3, 5, 5, and a random number?

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Suppose you had 5 regular dice. What are the odds of rolling a 2, 3, 5, 5, and a random number?

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Answer 1 · 2018-06-16T12:57:16

Odds of rolling 2, 3, 5, 5, and one other with 5 regular dice: $50%$

Explanation:

There are $5! =5xx4xx3xx2xx1$ possible outcomes of rolling 5 regular dice.

Of these possibilities there are
$color(white)("XXX")5$ choice for which die is the (first) 2 to appear,
and of the remaining 4 possibilities there are
$color(white)("XXX")4$ choices for which die is the (first) 3 to appear,
and of the remaining 3 possibilities there are
$color(white)("XXX")3$ choices for which are the (first two) 5's to appear.

So there are $5xx4xx3$ outcomes that represent the desired result.

Probability of the desired result $=(5xx4xx3)/(5xx4xx3xx2xx1)=1/2=50%$

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Suppose you had 5 regular dice. What are the odds of rolling a 2, 3, 5, 5, and a random number?

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