with three die what outcome has a greater probability a nine or a ten?

Question

if i have three dice what outcome will have a greater probability, rolling a nine or rolling a ten?

Answer 1

9=1+2+6, 1+3+5, 1+4+4, 1+5+3, 1+6+2, 2+1+6, 2+2+5, 2+3+4, 2+4+3, 2+5+2, 2+6+1, 3+1+5, 3+2+4, 3+3+3, 3+4+2, 3+5+1, 4+1+4, 4+2+3, 4+3+2, 4+4+1 (20 ways)

10=1+3+6, 1+4+5, 1+5+4, 1+6+3, 2+2+6, 2+3+5, 2+4+4, 2+5+3, 2+6+2, 3+1+6, 3+2+5, 3+3+4, 3+4+3, 3+5+2, 3+6+1, 4+1+5, 4+2+4, 4+3+3, 4+4+2, 4+5+1, 5+1+4, 5+2+3, 5+3+2, 5+4+1, 6+1+3, 6+2+2, 6+3+1 (27 ways)

Therefore the probability of rolling 10 is higher than the probability of rolling 9.

Probabilities: 9=20/216=5/54 (about 9.25%); 10=27/216=⅛ (12.5%).