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

Explanation

The question is asking about the count of three-digit numbers that can be formed with the digits, 1, 2, 3, 4, 5, 6, 7, 8 and 9 in ascending order only. Option 1 suggests there are 80 such numbers. This is not accounting for all the combinations possible. Option 2 recommends 81 such numbers. Again, all combinations have not been considered in this count. Option 3 insists there are 83 such numbers. Once more, the counting is not accurate as it is less than the actual count. Option 4 states there are 84 such numbers. This is indeed the correct count. With 9 digits, we want to find the number of ways to choose 3 to put in ascending order. The number of ways to pick 3 numbers out of 9 (order doesn`t matter) is given by the binomial coefficient “9 choose 3”, which is calculated as 9! / (3!(9-3)!) = 84. So, the correctly dissected answer is option 4 – 84.