Question

how many integers are between 1 and 1000 have distinct digits

Answer 1

there are Infinity number of integers between 1 and 1000

Answer 2

Concept:

Let's recall definitions of whole numbers and integers and permutations.

Whole numbers are natural numbers and 0.

Integers are the whole numbers which can be positive or negative.

Permutation is the concept of different arrangements of things by taking some or all of them at a time.

Given:

We are given integers 1 and 1000

To find:

We are asked to find many integers are there in between 1 to 1000 with distinct digits

Solution:

The integers between 1 and 1000 will be of 1 digit, 2 digits and 3 digits.

For one-digit numbers, there are 9 integers

For two-digit numbers, there are 81 integers deleting the integers like 11,22,33,44,55,66,77,88,99

For three-digit numbers, we will use permutation:

All the three digits have to be distinct, So, for the 100's place, we have 9 options for numbers from 1 to 9.

For the 10's place, we have 9 options excluding the number in the 100's place and including 0

For the 1's place, we have 8 options excluding the numbers in the 100's and 10's places.

So. the total three-distinct-digit numbers are 9x9x8=648

Hence, the total number of integers between 1 to 1000 with distinct digits are:

648+81+9=738

Conclusion:

There are 738 integers between 1 and 1000 with distinct digits