Math Problem - Need help - Permutations


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9 eligible bachelors and 6 single women buy tickets in the same 15-seat row theater. In how many ways can pairs of adjacent seats are ticketted to form eligible couples?

For example: A seating arrangement like M M F M M F M F F M F M F M M gives 10 possible pairs (i.e 5 MF pairs and 5 FM pairs).

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If you've got a casio calculator, you'll be wanting to use the C button, for choose.

e.g. 10c3 will give the the number of times 3 things can be picked from the 10 items.

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9 eligible bachelors and 6 single women buy tickets in the same 15-seat row theater. In how many ways can pairs of adjacent seats are ticketted to form eligible couples?

For example: A seating arrangement like M M F M M F M F F M F M F M M gives 10 possible pairs (i.e 5 MF pairs and 5 FM pairs).

Even MMMMMMMMMFFFFFF would produce 1 possible pair.

So could the question not be simplified to: how many different positions can you arrange 6 'identical items' (i.e. order doesn't matter) in a slot of 15? (or 9 items in 15 slots, which I assume would produce the same result)?

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