Question

find the number of permutations of the letters of the Hyderabad word Hyderabad​

Answer 1

SOLUTION :

TO DETERMINE

The number of permutations of the letters of the word HYDERABAD

EVALUATION

Here the given word is HYDERABAD

Now the letters and their numbers in the word HYDERABAD is as below

$\sf{}Letter : \: \: \: \: \: \: H \: \: \: Y \: \: \: D \: \: \: E \: \: \: R \: \: \: A \: \: \: B \: \: \: Total$

$\sf{}Number : \: \: 1 \: \: \: \: 1 \: \: \: \: 2 \: \: \: 1 \: \: \: \: 1 \: \: \: \: 2 \: \: \: \: 1 \: \: \: \: \: 9$

Hence the number of permutations of the letters of the word HYDERABAD is

$= \displaystyle \sf{} \frac{9 \: !}{ 1 \: ! \: 1 \: !\:2 \: ! \: 1 \: ! \: 1 \: ! \: 2\: ! \:1 \: ! }$

$= \displaystyle \sf{} \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}{ 2 }$

$\sf{} = 90720$

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