# How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

**Solution:**

The given word has 3 vowels (A, U, E) and 5 consonants (D, G, H, T, R).

We know that the number of ways of selecting r different things from n different things is a combination and is calculated using the formula ^{n}Cᵣ = n! / [r!(n−r)!]. Using this,

- No. of ways of selecting 2 vowels out of 3 vowels is ³C₂.
- No. of ways of selecting 3 consonants out of 5consonants is ⁵C₃.

By fundamental principle of counting,

The required number of ways = ³C₂ × ⁵C₃

= (3!) / [2! (3-2)!] × (5!) / [3! (5-3)!] (Using nCr formula)

= 3 × 10

= 30

NCERT Solutions Class 11 Maths Chapter 7 Exercise ME Question 1

## How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

**Summary:**

The number of words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER is 30