11.1.30

How many three-digit even numbers are possible if the leftmost digit cannot be zero?

The total number of 3 digit even numbers is 450

Step-by-step explanation:

Step 1:

We need to determine the number of 3 digit numbers which is even and the leftmost digit is not zero.

The 3 digits with left most digit not equal to zero starts from 100 and goes up to 998

If we consider only the even 3 digit numbers in this interval, this would form an arithmetic progression with the first number a = 100 and the common difference d = 2.

Step 2:

The last number l in this series is 998.

So we have

a = 100

l = 998

d = 2

The nth term in the arithmetic progression is given by a + (n-1) d

so substituting the above values we get

100 + (n-1) 2 = 998

2n = 900 = > n = 450

Step 3:

Answer:

The total number of 3 digit even numbers is 450