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

Answer 1

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 ⁴C₂ × ⁵C₃
$$\begin{gathered} =\frac{4!}{2!2!}\times \frac{5!}{3!2!} \\ =6\times 10=60 \end{gathered}$$
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.