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. 720

Home » 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. 720

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. 720

Solution:

Option (C) 7200 is correct.

Explanation:

It is known that,

${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}$

$=\frac{n !}{r !(n-r) !}$

4 be the total number of given vowel

5 be the total number of given consonant

Using 2 vowels and 3 consonants the total number of words that can be formed $= {}^4{C}_2$ $.{}^5{C}_3 = {4!/2!}\mathrm {2!}$

Two vowel and Three consonant $=5!$

The total no. of word $= {5!}\times {4!/2!2!} = 7200$

As a result, Option (C) 7200 is the correct answer.

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