Question

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?

Answer 1

Case1
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