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2015-04-26T20:24:25+05:30

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There are 10 letters in the word CALCULATOR.
Start by pretending that all the letters are different, then the total arrangements would be simply 10!

But, there are 2 C's,  2 A's, and 2 L's.
For each of these, there will be repititions, as swapping two same letters wont produce a different arrangement. There are 2! ways to swap C's,  2! ways to swap A's,  and 2! ways to swap L's. Dividing these duplicates gives the answer :
\dfrac{10!}{2!{\cdot}2!{\cdot}2!}
1 5 1
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