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Problem 393

Combinatorics Difficulty 2.0 Prove it UKMT Senior Kangaroo · United Kingdom · 2021

Billie has a die with the numbers 1, 2, 3, 4, 5 and 6 on its six faces. Niles has a die which has the numbers 4, 4, 4, 5, 5 and 5 on its six faces. When Billie and Niles roll their dice the one with the larger number wins. If the two numbers are equal it is a draw. The probability that Niles wins, when written as a fraction in its lowest terms, is $\frac{p}{q}$ . What is the value of $7p + 11q$ ?

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