Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2

1.	Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Answer» In this problem first, we have to select consonants and vowels. Then we arrange a five-letter word using 3 consonants and 2 vowels. Therefore here both combination and permutation involved. The number of ways of selecting 3 consonants from 7 is ⁷C₃. The number of ways of selecting 2 vowels from 4 is ⁴C₂. The number of ways selecting 3 consonants from 7 and 2 vowels from 4 is ⁷C₃ x ⁴C₂. Now with every selection number of ways of arranging 5 letter word = 5! x ⁷C₃ x ⁴C₂ = 120 x \(\frac{7\times6\times5}{3\times2\times1}\) x \(\frac{4\times3}{2\times1}\) = 25200

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Answer»

In this problem first, we have to select consonants and vowels.

Then we arrange a five-letter word using 3 consonants and 2 vowels.

Therefore here both combination and permutation involved.

The number of ways of selecting 3 consonants from 7 is ⁷C₃.

The number of ways of selecting 2 vowels from 4 is ⁴C₂.

The number of ways selecting 3 consonants from 7 and 2 vowels from 4 is ⁷C₃ x ⁴C₂.

Now with every selection number of ways of arranging 5 letter word

= 5! x ⁷C₃ x ⁴C₂

= 120 x \(\frac{7\times6\times5}{3\times2\times1}\) x \(\frac{4\times3}{2\times1}\)

= 25200