Q. 2 C5.0( 3 Votes )

In how many ways

Answer :

Given: the word is ‘STRANGE.’


To find: number of arrangements so that the vowels occupy only odd positions


Number of vowels in word ‘STRANGE’ = 2(E, A)


Number of consonants = 5(S, T, R, N, G)


Let vowels be denoted by V


Odd positions are 1, 3, 5 or 7


So, fix the position by Vowels like this:



Now, arrange these 2 vowels at 4 odd places


Formula used:


Number of arrangements of n things taken r at a time = P(n, r)



Total number of arrangements of vowels


= the number of arrangements of 4 things taken 2 at a time


= P(4, 2)




= 4 × 3


= 12


The remaining 3 even places and 2 odd places can be occupied by 5 consonants


So, arrange these consonants at these places


Formula used:


Number of arrangements of n things taken all at a time = P(n, n)



Total number of arrangements of consonants


= the number of arrangements of 5 things taken all at a time


= P(5, 5)




0! = 1}


= 5!


= 5 × 4 × 3 × 2 × 1


= 120


Hence, the number of arrangements so that the vowels occupy only odd positions = 12 × 120 = 1440


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