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+1 vote
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in Mathematics by (114k points)
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In what number of ways can the letters of the word 'ABLE' be arranged so that the vowels occupy even places?
1. 2
2. 4
3. 6
4. 8

1 Answer

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Best answer
Correct Answer - Option 2 : 4

Concept:

Number of ways to arrange n things in r places is given by, nCr 

 

Calculation:

In word ABLE, there are 2 vowels and 2 consonants.

Total number of letters = 4

Total number of even place = 2

There are 2 vowels to be filled in 2 places.

⇒ The number of ways = 2C2 = 1

 The vowels can arrange among themselves in 2! = 2 ways.

 The 2 consonants can fill the remaining 2 places in 2! = 2 ways.

 Total number of ways = 1 × 2 × 2 = 4 ways.

Hence, option (2) is correct.

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