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

Jun 16, 2018

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
$\textcolor{w h i t e}{\text{XXX}} 5$ choice for which die is the (first) 2 to appear,
and of the remaining 4 possibilities there are
$\textcolor{w h i t e}{\text{XXX}} 4$ choices for which die is the (first) 3 to appear,
and of the remaining 3 possibilities there are
$\textcolor{w h i t e}{\text{XXX}} 3$ choices for which are the (first two) 5's to appear.

So there are $5 \times 4 \times 3$ outcomes that represent the desired result.

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