noboru wrote:

Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his?

A. 24/64

B. 32/64

C. 36/64

D. 40/64

E. 42/64

Hi! Could anybody please help me to find where I am wrong?

We can get scores, that are larger than 10 in the following combinations:

11: 452, 443, 335, 551, 641

12: 336, 444, 543, 651, 552

13: 445, 553, 643, 652, 661

14: 554,644,662

15: 654, 555, 663

16: 655, 664

17: 665

18: 666

From those we have 7 combination that can be different in 6 ways, 15 in 3 ways and 3 in 1 way. Multiply each and then add together: 6*7=42, 3*15=45, 3. 45+42+3=90.

Probability: 90/216.