Question

Total number of words (with or without meaning) from letters of word LETTER if no two vowels are together? A)100 B) 110 C) 120 D) 180

Answer 1

Answer:

b

c

d.

is the answer

because a,e,i,o,u are vowels

Answer 2

Answer:

$\bigstar{\bold{Option\:C:120}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• The word LETTER

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Total number of words that can be formed from the word LETTER if no two vowels occur together

$\Large{\underline{\underline{\bf{Solution:}}}}$

➳ Number of letters in the word = 6

➳ But the letters T and E repeat 2 times.

➳ Hence the total number of words that can be formed from the word LETTER is

=  6 ! / 2! × 2 !

= 6 × 5 × 4 × 3 ! / 2 × 2

 = 180

➳ Let us take the two vowels E and E as one letter

➳ Hence the number of words formed where the vowels always come together

= 5 ! / 2 !

= 5 × 4 × 3 ! / 2

= 60

➳ Number of words that can be formed where no two vowels occur together = Total number of words that cam be formed - Number of words formed where vowels always occur together

➳ Substitute the datas,

   Number of words that can be formed where no two vowels occur together = 180 - 60

              = 120

➳ Hence the total number of words that can be formed where no two vowels occur together is 120

$\boxed{\bold{Number\:of\:words=120}}$

➳ Hence option C is correct.