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Rearranging a word

CombinatoricsEasy

How many distinct strings can be made by rearranging all the letters of $BANKING$ , counting strings that look identical only once?

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Hint

Start with the arrangements of distinct letters, then correct for the letter that repeats.

Solution

The word has $7$ letters, and only $N$ appears more than once, exactly $2$ times.
If all letters were distinct there would be $7! = 5040$ arrangements.
Swapping the copies of $N$ gives the same string, so each string was counted $2$ times.
The count is $5040 \div 2 = 2520$ .

Answer: $2520$