How many 2-digit numbers can be formed using the digits 1,2,3,4,5,6,7,8,9 and 0? No digit can be used more than once

10, 23, 45, 67, 89

To find the number of 2-digit numbers that can be formed using the given digits without repetition, we can use the concept of permutations.

Permutation is a way to arrange objects in a specific order. The formula for finding the number of permutations is given by nPr = n! / (n - r)!, where n represents the total number of objects and r represents the number of objects to be arranged.

In this case, we have 10 digits to choose from (0 to 9) and we need to form 2-digit numbers. Using the permutation formula, we can calculate as follows:

n = 10 (total number of digits)
r = 2 (2-digit numbers)

nPr = 10! / (10 - 2)!
= 10! / 8!
= (10 × 9 × 8!) / 8!
= 10 × 9
= 90

Therefore, there are 90 different 2-digit numbers that can be formed using the digits 1 to 9 and 0, without repeating any digit.