Question

Find the number of words those can be formed by using all letters of the word 'DAUGHTER'. If
(i) Vowels occurs in first and last place.
Start with letter G and end with letters H.
Letters G,H,T always occurs together.
(iv) No two letters of G,H,T are consecutive
No vowel occurs together
(vi) Vowels always occupy even place.
(vii) Order of vowels remains same.
(viii) Relative order of vowels and consonants remains same.
(ix) Number of words are possible by selecting 2 vowels and 3 consonants.​

Answer 1

Answer:

4320 words

720 words

2160  words

Step-by-step explanation:

DAUGHTER

Total - 8

A  E  U - 3 Vowels

D G H  R T = 5 Consonants

Vowels occurs in first and last place.

³P₂ = 6 ways

remaining 6 positions  in 6! ways

6! * 6  = 4320 words

Start with letter G and end with letters H

6!  = 720 words

Letters G,H,T always occurs together.

GHT  as 1  remaining 5 => total 6

GHT can be arranged in 3! ways

6! * 3!   = 2160  words