Answer
350.4k+ views
Hint: 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, 7
Therefore, there are a total of 5 digits.
Now, as we have to form 3 digit numbers, let us draw three boxes.
First box will be hundreds, the second box will be tens and the third box will be ones.
Now, as the number is 3 – digit, the first box cannot use digit 0, because if we use 0 as first digit, the number will not be a 3 digit number. So, only 4 digits that are 1, 3, 5 and 7 can be used in the first box.
Therefore, there are 4 ways to fill the first box.
Now, for the second box, any out of the 5 given digits can be used to fill the box as repetition is allowed.
Therefore,
And for the third box too, we can fill it using any of the 5 given digits. Therefore, we get
So, therefore the total ways for forming 3 digit number will be
$ \Rightarrow $Total ways of arrangement $ = 4 \times 5 \times 5 = 100$
Therefore, a total of $100$ 3 digit numbers can be formed using the digits 0, 1, 3, 5, 7 when repetition is allowed.
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$
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, 7
Therefore, there are a total of 5 digits.
Now, as we have to form 3 digit numbers, let us draw three boxes.
First box will be hundreds, the second box will be tens and the third box will be ones.
Now, as the number is 3 – digit, the first box cannot use digit 0, because if we use 0 as first digit, the number will not be a 3 digit number. So, only 4 digits that are 1, 3, 5 and 7 can be used in the first box.
Therefore, there are 4 ways to fill the first box.
Now, for the second box, any out of the 5 given digits can be used to fill the box as repetition is allowed.
Therefore,
And for the third box too, we can fill it using any of the 5 given digits. Therefore, we get
So, therefore the total ways for forming 3 digit number will be
$ \Rightarrow $Total ways of arrangement $ = 4 \times 5 \times 5 = 100$
Therefore, a total of $100$ 3 digit numbers can be formed using the digits 0, 1, 3, 5, 7 when repetition is allowed.
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$
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)