Question

How many even numbers can be formed using
the digits 2, 3, 7, 8 so that the number formed
is less than 1000?
​

Answer 1

Answer:

42 with repetition of digits is allowed,

and 20 if repetition of digits is not allowed .

Answer 2

There are 42 even numbers less than 1000 that can be formed using the digits 2,3,7, and 8.

Given,

The digits = 2,3,7 and 8.

The number formed should be an even number and less than 1000.

To Find,

The number of even numbers that can be formed using the digits.

Solution,

In this question, it is given that the numbers formed are even numbers.

So, let's understand the concept of even numbers.

Even numbers are those that are divisible by two, able to be divided into two equal groups or pairs. For example, 2, 4, 6, 8, 10, and so on. It is possible to group these numbers into equal pairs.

So, the number will only start with 2 or 8.

Now, let's solve the question,

Case:1 one- digit number

Possible digits = 2 or 8.

The number of ways = 2 ways.

Case:2 two-digit number

Possible digits on ten's place are 2,3,7,8

Possible digits on the unit place are 2,8

The number of ways = 4 × 2 = 8

Case:3 Three-digit number

Possible digits on hundredth's place are 2,3,7,8

Possible digits on ten's place are 2,3,7,8

Possible digits on the unit place are 2,8

The number of ways = 4 × 4 × 2 = 32

So, the total number of ways = 2 + 8 + 32

= 42.

There are 42 even numbers less than 1000 that can be formed using the digits 2,3,7, and 8.

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