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

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:

Number of vowels given is 4

Number of consonants given is 5

We have to form words by 2 vowels and 3 consonants number of  ways of selecting 2 vowels out of 4 is 4C2 number of  ways of selecting 3 consonants out of 5 is 5C3.

Hence number of ways of selection is 4C× 5C3

$=\frac{4 !}{2 ! 2 !} \times \frac{5 !}{3 ! 2 !}$

$=6 \times 10=60$

Now, there selected 5 letters can be arranged is 5! ways

So, total number of words is 60 × 5!

= 60 × 120

= 7200

Hence the correct answer is option C.