Answer VerifiedHint: As we have to form 3 – digit numbers, the first digit cannot be 0. So, the first digit can be arranged in 4 ways. Now, as repetition is allowed, the second and the third digit can be arranged in 5 ways. The total numbers formed will be equal to the product of these values. Complete step-by-step solution: In this question, we are asked how many 3 digit numbers can be formed using the digits 0, 1, 3, 5, 7 where repetition is allowed.Given digits: 0, 1, 3, 5, 7Therefore, there are a total of 5 digits.Now, as we have to form 3 digit numbers, let us draw three boxes.
And for the third box too, we can fill it using any of the 5 given digits. Therefore, we get
Note: Here, note that if repetition were not allowed, then we would have got different answers. For first digit:As we have to form a 3 digit number, we cannot use 0 as the first digit. So,For second digit:Now, suppose we used 1 as the first digit, so now it cannot be used again for the second and third digit. So, the second digit can be 0, 3, 5 or 7. Therefore, For third digit:Suppose we used 3 as the second digit, so now 3 cannot be used for the third digit. So, the third digit can be 0, 5 or 7. Therefore, $ \Rightarrow $Total numbers formed when repetition is not allowed$ = 4 \times 4 \times 3 = 48$ |