How many 5-digit numbers can be formed by using the digits 0, 1 and 2?

Answer»

Given: We have 3 digits, i.e. 0, 1 and 2

To Find: Number of 5-digit numbers formed

Let us represent the arrangement

2 ways, i.e. 1,2

3 ways

For forming a 5-digit number, we have to fill 5 vacant spaces.

But the first place cannot be filled with 0, hence for filling first place, we have only 1 and 2

First place can be filled with 2 numbers, i.e. 1, 2 = 2 ways

Second place can be filled with 3 numbers = 3 ways

Third place can be filled with 3 numbers = 3 ways

The fourth place can be filled with 3 numbers = 3 ways

The fifth place can be filled with 3 numbers = 3 ways

Total number of ways = 2 × 3 × 3 × 3 × 3 = 162

162 5-digit numbers can be formed by using the digits 0, 1 and 2.

Discussion