Question

Consider all the permutations of the word $BENGALURU$. The number of words in which vowels occur at even places is given as $A$ and the number of words in which the letters of the word $GLUE$ appear together in that order is given as $B$. Find the value of $A-B$

• A. $1440$
• B. $720$
• C. $2160$
• D. $1200$

Answer 1

The correct option is B $720$

No. of ways in which vowels$\{E,A,U,U\}$ can take even places in the word $BENGALURU$ is $\frac{4!}{2!}\times 5!=A=1440$

Consider $GLUE$ as a single entity.
Then, no. of ways in which $GLUE$ appears together is $6!=B=720$
$\Rightarrow A-B=720$