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The number of words (with or without meaning) that can be formed from all the letters of the word “BETTER” in which vowels never come together is

 

Option: 1

110


Option: 2

90


Option: 3

130


Option: 4

120


Answers (1)

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The word ‘BETTER’ has 6 letters in which 2 are repeated twice.

The total number of 6 letters word is given by,

\begin{aligned} &\frac{6 !}{2 ! 2}=\frac{6 \times 5 \times 4 \times 3 \times 2}{2 \times 2}\\ &\frac{6 !}{2 ! 2 !}=180 \end{aligned}


There are 2 vowels in the word that is (EE).

So, the vowels can be arranged in \frac{5 !}{2 !} ways.

Thus,

\begin{aligned} &\frac{5 !}{2 !}=\frac{5 \times 4 \times 3 \times 2}{2}\\ &\frac{5 !}{2 !}=60 \end{aligned}

Thus, the total number of words where vowels are not together is 180 - 60 = 120.

Therefore, the total number of ways the word is formed is 120 ways.

 

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