# How Many Different Words, Each Containing 2 Vowels and 3 Consonants Can Be Formed with 5 Vowels and 17 Consonants? - Mathematics

How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?

#### Solution

2 out of 5 vowels and 3 out of 17 consonants can be chosen in ${}^5 C_2 \times {}^{17} C_3$  ways.

Thus, there are ${}^5 C_2 \times {}^{17} C_3$groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters, which can be arranged in

$5!$  ways.
∴ Required number of words = $\left( {}^5 C_2 \times {}^{17} C_3 \right)5!$
$6800 \times 120 = 816000$
Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.3 | Q 1 | Page 23