Question

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

Answer 1

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%`