How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

Solution:

In the given word EQUATION,

• No. of vowels = 5 (E, U, A, I, O)
• No. of consonants = 3 (Q, T, N)

Let us consider that there are 2 units, one consisting of vowels and one of the consonants. i.e.,

No. of ways in which 5 vowels can be arranged among themselves = 5!

No. of ways in which 3 consonants can be arranged among themselves = 3!

No. of ways in which these two units can be arranged = 2!

The total number of ways = 2! × 3! × 5! = 1440

NCERT Solutions Class 11 Maths Chapter 7 Exercise ME Question 2

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

Summary:

The number of words, with or without meaning, that can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together is 1440