**Question**

**Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?**

A. 25200

B. 210

C. 24400

D. 21300

**Answer:** A

**Solution:**

Number of ways of selecting 3 consonants from 7 = 7C3

Number of ways of selecting 2 vowels from 4 = 4C2

Number of ways of selecting 3 consonants from 7 and 2 vowels from 4 = 7C3 × 4C2

= (7 × 6 × 53 × 2 × 1) × (4 × 32 × 1) = 210

It means we can have 210 groups where each group contains total of 5 letters (3 consonants and 2 vowels).

Number of ways of arranging 5 letters among themselves =5!

= 5 × 4 × 3 × 2 × 1 = 120 =5!

= 5 × 4 × 3 × 2 × 1 =120

Hence, required number of ways = 210 × 120 = **25200**