# What are the number of such words formed

Out of 7 consonants and 4 vowels,words are to be formed by involving 3 consonants and 2 vowels. The number of such words formed is :

- -25200
- 22500
- 10080
- 5040

**Answer: (1) 25200**

**Solution:-**

Number of ways of selecting 3 consonants out of 7 = ^{7}C_{3}

Number of ways of selecting 2 vowels out of 4 = ^{4}C_{2}

Number of ways of selecting 3 consonants out of 7 and 2 vowels out of 4 = ^{7}C_{3} x ^{4}C_{2
}=(7×6×5/3×2×1)×(4×32×1)=210

It means that we can have 210 groups where each group contains total 5 letters (3 consonants

and 2 vowels).

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

= 5 x 4 x 3 x 2 x 1 = 120

Then, Required number of ways = 210 x 120 = 25200

Hence, the correct answer is option (1) 25200.