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How many 3-letter words can be formed using the letters from the word GALE, if repetition is not allowed?
  • a)
    4
  • b)
    9
  • c)
    10
  • d)
    14
  • e)
    24
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
How many 3-letter words can be formed using the letters from the word ...
Given: 4-letter word GALE
To find: Number of 3-letter words that can be formed without repeating any letters
Approach:
We will use the method of filling spaces to answer the question
Working Out:
  1. Let’s draw the 3 spaces, to denote the 3-letter word we need to form: _ _ _
  2. The objective of forming the word requires 3 tasks:
    1. Task 1 – Fill Space 1
    2. Task 2 – Fill Space 2
    3. Task 3 – Fill Space 3
  3. Since each of these 3 tasks need to be done to make the 3-letter word, we will multiply the number of ways to do each task:
  4. Number of ways to fill Space 1 = 4 (G, A, L, E – all letters are available at this point)
  5. Number of ways to fill Space 2 = 3
  6. Number of ways to fill Space 3 = 2
  7. So, (Number of 3-letter words) = 4*3*2 = 24
 
Answer: Option E
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How many 3-letter words can be formed using the letters from the word GALE, if repetition is not allowed?a)4b)9c)10d)14e)24Correct answer is option 'E'. Can you explain this answer?
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