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

1 Answer
Jun 16, 2018

Answer:

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%#