# The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

**Solution:**

Given that the English alphabet has 5 vowels and 21 consonants.

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 from 5 vowels = ⁵C₂ = 10.
- No. of ways of selecting 2 consonants from 21 consonants = ²¹C₂ = 210.

No. of ways in which these 4 letters can be rearranged among themselves = 4! = 24.

By fundamental principle of counting,

Required number of words = 10 × 210 × 24 = 50400

NCERT Solutions Class 11 Maths Chapter 7 Exercise ME Question 6

## The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

**Summary:**

The total no. of words with two different vowels and 2 different consonants, if the English alphabet has 5 vowels and 21 consonants is 50,400