1. Find the number of permutations that can be had from the letters of the word 'OMEGA' such that
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Second step: O and A are two letters to be arranged = 3p2.2!
(Explanation: Two letters O and A can be arranged in three odd place in 3p2 ways.
Now, these two letters can be arranged among themselves in 2! ways.
So, no. of ways to arrange O and A = 3p2.2!)
Rest everything is same.
there are three odd places i.e=1,3,5
A and O are two letters to be arranged=3C2.2!
the other three letters can be arranged in 3! ways
so total ways=6X6=36 ways
2. Fix the E in the middle place the other four letters can be arranged in 4! ways=24
3.There are 3 vowels and three odd places so vowels can be arranged in 3! ways
the other 2 letters can be arranged in 2! ways
so total no. of ways=6X2=12
4.for the two consonents there are 2! ways and vowels can be arranged between them in 3! ways
total no. of ways = 2X6=12