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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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?

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Test: Permutation And Combination- 2

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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:

Let’s draw the 3 spaces, to denote the 3-letter word we need to form: _ _ _
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
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:
Number of ways to fill Space 1 = 4 (G, A, L, E – all letters are available at this point)
Number of ways to fill Space 2 = 3
Number of ways to fill Space 3 = 2
So, (Number of 3-letter words) = 4*3*2 = 24

Answer: Option E

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