How many 4-digit numbers are there with no digit repeated?

Solution:

We have to find the number of 4-digit numbers with no digits repeated.

The total number of digits = 10 (0 to 9)
No. of ways of choosing first digit = 9 (as 0 cannot be the first digit)
No. of ways of choosing second digit = 9
No. of ways of choosing third digit = 8
No. of ways of choosing fourth digit = 7

Using the fundamental principle of counting,
Total possible number of ways = 9×9×8×7 = 4,536

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.3 Question 2

How many 4-digit numbers are there with no digit repeated?

Summary:

The number of 4-digit numbers with no digits repeated is 4,536