Question

If two dice are thrown $5$ times what is the probability that sum of the numbers coming up will be $10$ in exactly $2$ out of these $5$ trials.

Answer 1

For sum to be 10 possible outcomes are(4,6),(5,5)(6,4)

Total pairs are 36

Probability that sum will be 10 in exactly two of 5=$=\frac{{{36}_C}_3\ast {3_C}_2}{{{36}_C}_5}=\frac{20\ast 3}{32\ast 31}=\frac{15}{248}$