Question

Suppose in a dice game, the person who rolls two dice wins if his rolls results in a pair of numbers whose sum is 7 or 11. In how many ways can he or she win

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c} & 1 &2 & 3 & 4 & 5 & 6 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hdashline 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hdashline 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hdashline 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hdashline 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ \hdashline 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hdashline \end{array}$$

$$6+2=8$$

The person can win in 8 ways:

$$1+6, 2+5, 3+4, 4+3, 5+2, 5+6, 6+1, 6+5$$