Question

find the words formed with or without meaning using the letter 'ENGLISH' such that vowels are together.​

Answer 1

Answer:

we have to separate the consonants and vowels and consider each time the set of the consonants and vowels as a single letter.

now,

here, word is E Q U A T I O N

vowels —> E , U, A , I , O ( there are five vowels in given words )

consonants—> T, Q , N ( there are 3 consonants in given words )

the vowels can be arranged in 5! ways

the consonants can be arranged in 3! ways

These vowels and consonants ( when we take as a single letter )can be arranged 2! ways .

hence, a/c to fundamental principle of counting

total number of ways =5!×3!×2!

=(5×4×3×2)×(3×2)×(2)

=120×6×2

=1440