Question

Find the number of unique permutations of the letters in each word.
5) CORRIDOR
6) NUMBER

Answer 1

Answer:

Ur Answer is 5 one CORRIDOR

Answer 2

The number of unique permutations of the letters CORRIDOR is 3360

The number of unique permutations of the letters NUMBER is 720

What is Permutation?

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items in a certain order.

$\frac{n!}{mA!mB!......mZ!}$

In the given word

CORRIDOR

There are 7 letters in which "O" repeats 2 times and "R" repeats 3 times.

Then n = 7 , A = 2 and B = 3

Put values in above formula

Then,

=  $\frac{7!}{2!3!}$

= $\frac{7\times6\times5\times4\times3\times2\times1}{2\times3\times2}$

= 3360

Similarly

NUMBER

There are 6 letters in which no letter repeats

means A = B = .......= Z = 1

Put values in above equation

= $6!$

= 720

Hence,

The number of unique permutations of the letters CORRIDOR is 3360.

The number of unique permutations of the letters NUMBER is 720.

Learn more about permutation:

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