18) In how many ways can the letters of the word 'INTERMEDIATE' be arranged so that
the vowels always occupy even places?
the vowels always occupy odd places?
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when vowels occupy only even places
no of vowels=6
no of even places=6
so no of ways they can be arranged=P(6,6)
6!/(6-6)!
=6!/0!
=6*5*4*3*2*1/1
=720
no of ways another letter can be arranged=P(6,6)=720
so no of ways they can be arranged=720*720
in same way for odd places we can get
when vowels occupy only even places
no of vowels=6
no of even places=6
so no of ways they can be arranged=P(6,6)
6!/(6-6)!
=6!/0!
=6*5*4*3*2*1/1
=720
no of ways another letter can be arranged=P(6,6)=720
so no of ways they can be arranged=720*720
in same way for odd places we can get
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