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In how many ways the letters of the word 'CIRCUMSTANCES' can be arranged such that all vowels came at odd places and N always comes at end?

Correct Answer: 1,51,200 ways.

Explanation:

In circumcstances word there are 3C's, 2S's, I, U,R, T, A, N, E


Total = 13 letters


But last letter must be N


Hence, available places = 12


In that odd places = 1, 3, 5, 7, 9, 11


Owvels = 4


This can be done in 6P4 ways 


Remaining 7 letters can be arranged in 7!/3! x 2! ways


 


Hence, total number of ways = 6P4 x 7!/3! x 2! = 360 x 5040/12 = 1,51,200 ways.


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