1 Find the number of permutations that can be had from the letters of the word 'OMEGA' such that - Maths - Permutations and Combinations

Question

1 Find the number of permutations that can be had from the
letters of the word 'OMEGA' such that
i) O & Aoccupy odd places
ii) E always occupies the middle place
iii) Vowels occupy odd places
iv) All the vowels are never together

Santosh Kumar · Accepted Answer

Dear Student Your friend has provided the correct answer
@Harmeet: Good effort! Keep posting!
For part(1):
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
Got it!

1. Find the number of permutations that can be had from the letters of the word 'OMEGA' such that i) O & Aoccupy odd places ii) E always occupies the middle place iii) Vowels occupy odd places iv) All the vowels are never together

1. Find the number of permutations that can be had from the letters of the word 'OMEGA' such that

i) O & Aoccupy odd places

ii) E always occupies the middle place

iii) Vowels occupy odd places

iv) All the vowels are never together