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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?

In what number of ways can the letters of the word 'ABLE' be arranged so that the vowels occupy even places? Correct Answer 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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