# Total Number of Words Formed by 2 Vowels and 3 Consonants Taken from 4 Vowels and 5 Consonants is Equal to (A) 60 (B) 120 (C) 7200 (D) None of These - Mathematics

MCQ

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

#### Options

• 60

• 120

• 7200

• none of these

#### Solution

7200
2 out of 4 vowels can be chosen in 4C2 ways and 3 out of 5 consonants can be chosen in 5Cways.
Thus, there are $\left( C_2 \times {}^5 {C^4}_3 \right)$ groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters that can be arranged in 5! ways.
∴ Required number of words =$\left( {}^4 C_2 \times {}^5 C_3 \right) \times 5! = 60 \times 120 = 7200$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 11 | Page 25