Question

how many 5 letter word containing 3 vowels and 2 consonants can be formed using the letters of worf ' EQUATION' so that the two consonant occur together ?

Answer 1

The answer is YES because you are talking about words and even if a single letter changes it’s place then a new word is formed.

So, you have C(21,5) x C (5,2) and these 5 selections can be rearranged, therefore multiplying the result by 5! is a good idea.

Finally, C(21,5) x C (5,2) x 5!

20349 x 10 x 120

24418800 is the answer

Answer 2

The word EQUATION contains 5 vowels and 3 consonants.

Number of ways of choosing 3 vowels from 5 is C(5, 3).

Number of ways of choosing 2 consonants from 3 is C(3, 2).

Number of ways of selecting 5 vowels and 3 consonants is C(5, 3)×C(3, 2)

Number of different words formed by these 5 letters is 5!

So the answer is C(5, 3)×C(3, 2)×5!

= 10×3×120

= 3600 words

Hope this will helps you....