in how many ways can the letter of the word 'MACHINE' be arranged so that the vowels may occupy only odd positions ?

Dear RAjan,

No of ways vowels can be arranged in odd positions = (4*3*2)
No of ways consonents can be arranged remaining positions = (4*3*2*1)

Total ways = (4*3*2)*(4*3*2*1) = 24*24=576

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