The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

Concept:

Permutations and Arrangements:

• A permutation is an arrangement of objects in a specific order. The number of ways to arrange 'n' objects is given by the factorial of 'n' denoted by n!.
• For a set of distinct vowels and consonants, the total number of ways to arrange them can be calculated by multiplying the factorials of the number of vowels and consonants separately.

Calculation:

Given the word 'EQUATION', we have:

• 5 vowels: A, E, I, O, U
• 3 consonants: Q, T, N

⇒ Number of ways = (3!) . (5!)

⇒ Numbers of ways = (3!) . (5!)

⇒ Total required number of ways = (3!) . (5!) + (3!) . (5!)

= 1440

∴ Option (c) is correct.