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Vandaag is het 19 September 2018

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Fairy tales - math puzzle

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A sultan has 14 daughters. He decides to tell every night four of his daughtes a fairy tale, but in such a way that every night, there will be another combination of four daughters. How many nights will keep the sultan busy telling fairy tales?

Explanation

Name the daughters of the sultan A,B,C,..., I. On a particular day the sultan can choose in 14 * 13 * 12 * 11 ways 4 daughters. In total this are 24024 combinations. But some of the combinations are equalt, that is if for example A, C, D, and F are listening to a fairy tale, this is the same as F, C, D, and A. There are 4 * 3 * 2 * 1 = 24 permuations which are equal. So in total there are 24024 / 24 = 1001 distinct combinations. The sultan will hence tell fairy tales for 1001 nights.