Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

Solution:

We have to find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated.

Total number of digits available = 5 (from 1 to 5)
No. of ways of choosing first digit = 5
Since no digit should be repeated,
No. of ways of choosing second digit = 4
No. of ways of choosing third digit = 3
No. of ways of choosing fourth digit = 2
Using the fundamental principle of counting,
Total possible number of ways = 5×4×3×2 = 120

For the number to be even the last digit must be either 2 or 4.
No. of ways of choosing last digit = 2
Since no digit should be repeated,
No. of ways of choosing first digit = 4
No. of ways of choosing second digit = 3
No. of ways of choosing third digit = 2
Using the fundamental principle of counting,
Total possible number of ways that will be even number =2×4×3×2=48

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.3 Question 4

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

Summary:

• The number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated is 120
• Among them, 48 are even