How many 3-digit even numbers can be made using the digits 1 2 3 4 6 if no digit is repeated?

Solution:

We have to find the number of 3-digit even numbers that can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated.

The total number of digits available = 6 (which are 1, 2, 3, 4, 6, 7). For the number to be even the last digit must be 2, 4, or 6. So no. of ways of choosing last digit = 3 As no digit should be repeated, No. of ways of choosing first digit = 5 

No. of ways of choosing second digit = 4

Using the fundamental principle of counting,
Total possible number of ways = 3×5×4 = 60

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.3 Question 3

Summary:

The number of 3-digit even numbers that can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated is 60

Calculations:

A three-digit even number is to be formed from given 6 digits 1, 2, 3, 4, 6, 7

The number at one's place can be filled by 2, 4, 6. 

Since repetition is not allowed

Now, Tens place can be filled by the remaining 5 digits

So, Tens place can be filled in 5 ways

Similarly, Hundred place can be filled by the remaining 4 digits

So, Hundred place can be filled in 4 ways

So, the Required number of ways in which three-digit even numbers can be formed from the given digits is 

⇒ Number of ways = 5 × 4 × 3

⇒ Number of ways = 60

 ∴ The required number of ways formed using 3- digit even number using 1, 2, 3, 4, 6, 7 is 60.