Four girls bought each a swimsuit , and they decided to share them . How many days are needed so that each girl will wear each swimsuit once ?
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1Does the order matter, or do you just want the possible top-5 groups? (I assume the order matters, but it’s worth asking.) // Please add the self-study tag, read its wiki, and say what progress you’ve made with this. We help with plenty of homework problems here, but we handle them differently from other questions. // Welcome to Cross Validated! – Dave Apr 04 '21 at 22:56
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If order doesn't matter: $15,504;$ if so, $1,860,480.$ What justification? – BruceET Apr 05 '21 at 02:03
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If order matters, there are 20 ways to choose 1st place, 19 ways to choose 2nd place, ..., 16 ways to choose 5th place: ${}_{20}P_5 = 20(19)\cdots(16) = 1\,860\,480.$ [Computation in R.]
prod(20:16)
[1] 1860480
If order does not matter: ${}_{20}C_5={20\choose 5} = \frac{20!}{5!\cdot15!} = 15\,504.$
choose(20, 5)
[1] 15504
BruceET
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