Question

How many 3-digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?

Answer 1

Hint: We are given 6 digits and we have to form 3 digit numbers. For the hundred’s place we have to choose any one of four of the digits 1,3,5,7. For the one’s and ten’s place we can choose any one digit of the five digits given. So, the total number of 3 digit numbers can be found by multiplying the number of possibilities.

Complete step-by-step answer:
Here, we are given 5 digits that are 0,1,3,5,7 and we have to form 3 digit number. For hundred’s place, we can choose any digit from 1, 3, 5, 7 . So, we have 4 intakes for the hundred’s place.
Also, we have to find the number of intakes for one’s place and ten’s place. For one’s place, we can choose any one digit from 0, 1, 3, 5, 7 . It means we have 5 intakes for the one’s place. Similarly, for
the ten’s place we have to choose any digit from 0, 1, 3, 5, 7. It means we have 5 intakes for the ten’s place. Let us understand with a diagram.

The total number of 3 digit numbers \[=4\times 5\times 5=100\] .

Note:In this question, the common mistake that can be done is taking “0” in the hundred’s place. As numbers consist of any digit from 0 to 9. But we cannot take 0 in the first place. If we do so then our number will be a two-digit number. But we have to form a 3-digit number. So, we have to ignore “0” to be included in the first place.