1.

In how many ways the letters of the word 'PIANO' can be arranged such that no consonant come together?1. 642. 723. 844. 96

Answer» Correct Answer - Option 2 : 72

Concept:

  • The ways of arranging n different things = n!
  • The ways of arranging n things, having r same things and rest all are different = \(\rm n!\over r!\)
  • The no. of ways of arranging the n arranged thing and m arranged things together = n! × m!
  • The number of ways for selecting r from a group of n (n > r) = nCr 
  • To arrange n things in an order of a number of objects taken r things = nPr  

 

Calculation:

For no consonants to be together the word can be formed as 

'1' A '2' I '3' O '4', where 1, 2, 3, 4 are the places where 2 consonants P and N could be placed

∴ Vowels arranged in = 3! ways

Ways of arranging consonants = 4P2

The total number of ways formed N = 3! × 4P2 

N = 6 × 12 = 72


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