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How many different ways are there of arranging the letters in the word ACCOMMODATION if no two Cs may be together?

Answer 1

Eva Abramson

#109771200#

ACCOMMODATION has #13# letters comprising:

If the letters were all different, then there would be #13!# ways of arranging them.

As it is, the total number of distinct ways of arranging all #13# letters is:

#(13!)/(3!2!2!2!) = 6227020800/(6*2*2*2) = 6227020800/48 = 129729600#

If the two letter C's are adjacent, then it is as if we are arranging #12# objects, with:

The number of ways that we can do that is:

#(12!)/(3!2!2!) = 479001600/(6*2*2) = 479001600/24 = 19958400#

So the total number of ways of arranging the letters of ACCOMMODATION with no #2# C's together is:

#129729600 - 19958400 = 109771200#

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Answer 2

Jace Anderson

To find the number of arrangements of the word "ACCOMMODATION" where no two Cs are together, we treat the two Cs as a single unit. So, we have 10 letters in total, where "CC" is considered as one letter. Therefore, the number of arrangements is ( \frac{10!}{2!} = 1,814,400 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.