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Dmitri has a pair of standard dice; one die is blue, and the other die is yellow. He rolls both of his dice. How many ways could the number on the blue die be larger than the number on the yellow die?

May 1, 2018

#1
+22581
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Dmitri has a pair of standard dice; one die is blue, and the other die is yellow.

He rolls both of his dice.

How many ways could the number on the blue die be larger than the number on the yellow die?

$$\begin{array}{|r|c|c|c|c|c|c|} \hline & \color{orange} 1 & \color{orange}2 & \color{orange}3 & \color{orange}4 & \color{orange}5 & \color{orange}6 \\ \hline \color{blue}1 & \\ \hline \color{blue}2 & \color{blue}2 > \color{orange}1 \\ \hline \color{blue}3 & \color{blue}3 > \color{orange}1 & \color{blue}3 > \color{orange}2 \\ \hline \color{blue}4 & \color{blue}4 > \color{orange}1 & \color{blue}4 > \color{orange}2 & \color{blue}4 > \color{orange}3 \\ \hline \color{blue}5 & \color{blue}5 > \color{orange}1 & \color{blue}5 > \color{orange}2 & \color{blue}5 > \color{orange}3 & \color{blue}5 > \color{orange}4 \\ \hline \color{blue}6 & \color{blue}6 > \color{orange}1 & \color{blue}6 > \color{orange}2 & \color{blue}6 > \color{orange}3 & \color{blue}6 > \color{orange}4 & \color{blue}6 > \color{orange}5 \\ \hline \end{array}$$

15 ways

May 2, 2018