The probability of getting 10 in a single throw of three fair dice is :

Exhaustive no. of cases = http://www.w3.org/1998/Math/MathML"><msup><mn>6</mn><mn>3</mn></msup></math> ;">6363

10 can appear on three dice either as distinct number as following (1, 3, 6) ; (1, 4, 5); (2, 3, 5) and each can occur in 3! ways. Or 10 can appear on three dice as repeated digits as following (2, 2, 6), (2, 4, 4), (3, 3, 4) and each can occur in http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>!</mo></mrow><mrow><mn>2</mn><mo>!</mo></mrow></mfrac></math> ;">3!2!3!2! ways .

http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> ;">∴∴ No. of favourable cases http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>×</mo><mn>3</mn><mo>!</mo><mo>+</mo><mn>3</mn><mo>×</mo><mfrac><mrow><mn>3</mn><mo>!</mo></mrow><mrow><mn>2</mn><mo>!</mo></mrow></mfrac><mo>=</mo><mn>27</mn></math> ;">=3×3!+3×3!2!=27