How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order?

Question

When digits must be in ascending order, once we select any 3 distinct digits from the available 9, there is only one way to arrange them—in ascending order. This reduces the problem to finding the number of 3-digit combinations from 9 digits. Using combinations: C(9,3) = 9!/(3!×6!) = 84. Therefore, 84 such three-digit numbers exist.

GKToday Admin · Accepted Answer

84 When digits must be in ascending order, once we select any 3 distinct digits from the available 9, there is only one way to arrange them—in ascending order. This reduces the problem to finding the number of 3-digit combinations from 9 digits. Using combinations: C(9,3) = 9!/(3!×6!) = 84. Therefore, 84 such three-digit numbers exist.

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