How many numbers with two or more digits can be formed
How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?
Answer
As the digits appear in ascending order in the numbers, number of ways of forming a n-digit number using nine digits = 9Cn
Number of possible two-digit numbers which can be formed
= 9C2 + 9C3 + 9C4 + 9C5 + 9C6 + 9C7 + 9C8 + 9C9
= 29 − (9C1 + 9C1)
= 512 − (1 + 9)
= 502
The correct answer is 502.