How many different words can be formed of the letter of word
“GRANDMOTHER”, so that:
(i) The word starts with G and end with R.
(ii) The letters A, N, D are always together.
(iii) All vowels never come together.
Answers
Given : GRANDMOTHER
To Find : How many different words can be formed of the letter of word
“GRANDMOTHER”
(i) The word starts with G and end with R.
(ii) The letters A, N, D are always together.
(iii) All vowels never come together.
Solution:
GRANDMOTHER
Vowels = 3
Consonants = 8 ( R repeated)
Total = 11
(i) The word starts with G and end with R
remaining 9 letters can be arranged in 9 ! words
= 362880 words
(ii) The letters A, N, D are always together.
(AND) as 1 can be in 3! = 6 ways
remaining 8
8 + 1 = 9 can be in 9! /2! ( as R is repeated)
= 6 * 9! /2!
= 10,88,640 words
(iii) All vowels never come together.
Total Words = 11!/2!
All vowels come together (A O E)
= 3! * 9! /2!
All vowels never come together. = 11!/2! - 6 * 9! /2!
= 1,88,69,760
Learn More:
How many words, With or without meaning, each of 2 vowels and 3 ...
brainly.in/question/6632198
In how many ways can the letters of the word "COMPUTER" be ...
brainly.in/question/14235713