Question

Find out how many distinct three-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order.

Answer 1

Given:

Digits = 1, 2, 3, 4, 5, 6, 7, 8, 9

To find:

3 digit numbers that can be formed using these digits such that the digits are in ascending order.

Solution:

Number of ways to choose 3 digits from 9 numbers without repetition:

= ⁹C₃ = 84

There would only be a single way in which the digits are arranged in ascending order.

For example if we have selected 3 digits: 8, 5, 3

Then there is only one way to arrange them in ascending order, and the number is 853.

Therefore 84 numbers can be formed.