How many ordered pairs of face values on two fair six-sided dice sum to 7?

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Multiple Choice

How many ordered pairs of face values on two fair six-sided dice sum to 7?

To sum to 7 with two fair six-sided dice, count all ordered outcomes where the first die shows a value x and the second shows 7−x. For x = 1,2,3,4,5,6, the paired values are 6,5,4,3,2,1 respectively, all valid faces. This gives six ordered pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Therefore there are six possibilities. Five would miss one of these pairs, four would only count unordered pairs, and seven would add an impossible extra, so six is correct.

To sum to 7 with two fair six-sided dice, count all ordered outcomes where the first die shows a value x and the second shows 7−x. For x = 1,2,3,4,5,6, the paired values are 6,5,4,3,2,1 respectively, all valid faces. This gives six ordered pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Therefore there are six possibilities.

Five would miss one of these pairs, four would only count unordered pairs, and seven would add an impossible extra, so six is correct.

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