Answer
384.6k+ views
Hint: To solve these types of problems based on the permutation of letters, we need to first find the number of letters that can be placed at each position. Then multiplying these numbers, we get the total numbers of words that can be formed. One should keep in mind that whether the repeating of letters is allowed or not, as the answer will change accordingly.
Complete step by step solution:
We are asked to form a five-letter word using the letters of the word TRICK. As all the letters of the word are distinct, we need to place the five letters in five positions. We are also given that the middle letter should be C, and the repeating of letters is not allowed.
For the first position, we can fill all five letters except C, hence the number of letters that can be filled is 4. For the second position, we can fill any of the left four letters except C, hence the number of letters that can be filled is 3. For the third position, we need C in the middle, so the number of letters that can be filled is 1. For the fourth position, we can fill any of the left two letters, hence the number of letters that can be filled is 2. For the last position, only one letter will be remaining, so the number of letters that can be filled is 1.
The number of words that can be formed equals the product of all numbers:
\[\Rightarrow 4\times 3\times 1\times 2\times 1=24\]
So, the correct answer is “Option C”.
Note: Here we are decreasing the number of letters for every next position because the repeating of letters is not allowed. If repeating is allowed, then we do not have to keep reducing the number of letters. This should be remembered.
Complete step by step solution:
We are asked to form a five-letter word using the letters of the word TRICK. As all the letters of the word are distinct, we need to place the five letters in five positions. We are also given that the middle letter should be C, and the repeating of letters is not allowed.
For the first position, we can fill all five letters except C, hence the number of letters that can be filled is 4. For the second position, we can fill any of the left four letters except C, hence the number of letters that can be filled is 3. For the third position, we need C in the middle, so the number of letters that can be filled is 1. For the fourth position, we can fill any of the left two letters, hence the number of letters that can be filled is 2. For the last position, only one letter will be remaining, so the number of letters that can be filled is 1.
The number of words that can be formed equals the product of all numbers:
\[\Rightarrow 4\times 3\times 1\times 2\times 1=24\]
So, the correct answer is “Option C”.
Note: Here we are decreasing the number of letters for every next position because the repeating of letters is not allowed. If repeating is allowed, then we do not have to keep reducing the number of letters. This should be remembered.
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)