Question

How many 5 letter words containing 3 vowels and 2 consonants can be
formed using the letters of the word EQUATION so that 3 vowels always
occur together?

Answer 1

Solution :-

There are 5 vowels from which 3 can be selected in 5p3 ways. 

There are three consonants from which 2 can be selected in 3p2 ways 

The three vowels can be interchanged in 3! ways and the whole 3 entities (3 vowels taken as one and the other 2 consonants) can be arranged in 3! ways.

So, total number of ways = 5p3 × 3p2 × 3! × 3!

⇒ (5*4*3)/(3*2*1) × (3*2*1)/(2*1) × (3*2*1) × (3*2*1)

⇒ (60/6) × (6/2) × 6 × 6

⇒ 10 × 3 × 6 × 6

⇒ 1080 ways

Answer.