The number of permutations of the letters of the word "ENGINEERING" is

\frac{11!}{3! 2!}

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\frac{11!}{(3! 2!)^{2}}

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\frac{11!}{(3!)^{2} .2!}

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\frac{11!}{3! (2!)^{2}}

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Solution

The correct option is B $\frac{11!}{(3! 2!)^{2}}$
Given word $E N G I N E E R I N G$
no of times each letter of the given word is repeated
$E = 3$
$N = 3$
$G = 2$
$I = 2$
$R = 1$

So, the total no. of permutations

= $\frac{11!}{3! 3! 2! 2! 1!}$

= $\frac{11!}{(3! 2!)^{2}}$

$∴$ the total no. of permutations $= \frac{11!}{(3! 2!)^{2}}$

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