In how many different ways can the letters of the word 'LEADING' be arranged…
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In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Answer: C. 720 — Key idea: Treat the three vowels A, E, I as a single block so they remain together. Step 1: Consider the vowel block plus the four consonants L, D, N, G. That…
- A.
360
- B.
480
- C.
720
- D.
5040
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Show answer & explanation
Correct answer: C
Key idea: Treat the three vowels A, E, I as a single block so they remain together.
Step 1: Consider the vowel block plus the four consonants L, D, N, G. That gives 5 objects to arrange, which can be done in 5! = 120 ways.
Step 2: Inside the vowel block, the three vowels A, E, I can be arranged in 3! = 6 ways.
Step 3: Multiply the arrangements of the blocks by the internal vowel arrangements: 5! × 3! = 120 × 6 = 720.
Answer: 720
Note: 5040 = 7!, which counts all permutations when there is no restriction. That does not satisfy the requirement that the vowels must come together.