# Probability question with dice

Three standard dice are rolled and the numbers thrown are added. what is the probability of getting a sum of 15?

• How would you approach this question? Do you have any solution-plan in mind? – Studentmath Apr 23 '14 at 11:37
• Unfortunately not. – Aspiring Mathlete Apr 23 '14 at 12:02

I don't see any easier way than going over all options and summing the probabilities:

Probability $\frac{3!}{6^3}=\frac{1}{36}$:

4,5,6

Probability $\frac{3}{6^3}=\frac{1}{72}$:

3,6,6

Probability $\frac{1}{6^3}=\frac{1}{216}$:

5,5,5

All together, you get $\frac{5}{108}$.

• $\frac{2!}{6^3}=\frac{1}{72}$? – robjohn Apr 23 '14 at 13:24
• $\frac{2!}{6^3} = \frac{1}{108}$ Giving you $\frac{1}{24}$ and not $\frac{5}{108}$ – User011123521 Apr 23 '14 at 13:30
• The number of variations of 3,6,6 is $\frac{3!}{2! \cdot 1!}=3$ not 2! – callculus Apr 23 '14 at 13:52
• @robjohn - that was a mistyping. the probability is $\frac{1}{72}$, but I wrote $2!$ instead of $3$. The final answer is true as well. – R B Apr 23 '14 at 14:44
• @RB: I noticed that you got the right answer, so I figured it was a typo. – robjohn Apr 23 '14 at 15:26