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How many different 3-letter words can be formed from the letters L, M, N, O, P, and Q without repeating any letter? It is not necessary for the words to have meaning per the English dictionary.
  • a)
    15
  • b)
    18
  • c)
    20
  • d)
    120
  • e)
    216
Correct answer is option 'D'. Can you explain this answer?
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How many different 3-letter words can be formed from the letters L, M,...
Understand the objective
  • Find the different 3 letter word that can be formed using the letters  L, M, N, O, P and Q.
  • (For example, words like LMN, MNP, LNM, PNQ etc.) 
 
  • Note that repetition of these letters is not allowed while framing a unique 3-letter word.
  • (For example, numbers like PPQ, LLL, OPO etc. are not allowed) 
 
  • As we are arranging letters here to form unique 3-letter words this is clearly a permutation problem. 
 
  • We can either use Filling Space method or Permutation Formula to solve this problem.
 
Method 1: Filling Space method
Write the objective equation enlisting all tasks
There is a total of 6 letters: L, M, N, O, P and Q
To accomplish the objective of forming 3-letter words, three task needs to be done:
·       Task1: Selecting a letter for the first space
o   This task can be achieved in 6 ways.
(We can choose any of the six letters)
·       Task2: Selecting a number for the second space
o   This task can be achieved in 5 ways.
(We can choose among the remaining 5 letters since we already selected one for the first space)
·       Task3: Selecting a number for third space
o   This task can be achieved in 4 ways.
(We can choose among the remaining 4 letters since we already selected two one for the first space and other for the second space) 
All these three tasks must be done to form three letter word.
 
Therefore, 
  • The objective of forming unique 3-letter word can be found by multiplying the number of ways in which each task is achieved.
 
Therefore,
·       No: of ways by which unique 3-letter words can be formed = 6 x 5 x 4 = 120 ways.
Correct Answer: Option D
Method 2: Permutation Formula
We can also use the permutation formula (nPr) to find our answer.
Out of the given six letters (L, M, N, O, P, Q) we have to arrange three letters so as to make a unique 3-letter word.
Therefore, 
  • n = 6 and r = 3
Hence, the number of ways by which unique 3-digit numbers can be formed 
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Most Upvoted Answer
How many different 3-letter words can be formed from the letters L, M,...
To find the number of different 3-letter words that can be formed from the letters L, M, N, O, P, and Q without repeating any letter, we can use the concept of permutations.

Permutations are arrangements of objects in a specific order. In this case, we want to find the number of permutations of 3 letters from a set of 6 letters.

Formula for Permutations:
The number of permutations of n objects taken r at a time is given by the formula:
P(n, r) = n! / (n - r)!

where n! denotes the factorial of n, which is the product of all positive integers less than or equal to n.

Let's apply this formula to solve the problem.

Step 1: Determine the values of n and r.
In this case, we have 6 letters (L, M, N, O, P, Q) and we want to find the number of permutations of 3 letters. So, n = 6 and r = 3.

Step 2: Calculate the factorial values.
n! = 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
(n - r)! = (6 - 3)! = 3! = 3 x 2 x 1 = 6

Step 3: Substitute the values into the formula.
P(6, 3) = 720 / 6 = 120

Therefore, there are 120 different 3-letter words that can be formed from the letters L, M, N, O, P, and Q without repeating any letter.

Answer: Option D) 120
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How many different 3-letter words can be formed from the letters L, M, N, O, P, and Q without repeating any letter? It is not necessary for the words to have meaning per the English dictionary.a)15b)18c)20d)120e)216Correct answer is option 'D'. Can you explain this answer?
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