Find the chance that the 5 people have 5 different birthdays. Here is my workings but I think I have gone wrong somewhere 364/365*364/365*363/365*362/365*361/365= I can't seem to get it right have I calculated something wrong?

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Find the chance that the 5 people have 5 different birthdays. Here is my workings but I think I have gone wrong somewhere 364/365*364/365*363/365*362/365*361/365= I can't seem to get it right have I calculated something wrong?

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= 1 - probability that 2 people have the same birthday
sorry, rephrase: = 1-[(probability that any 2 people have the same birthday)+(probability that any 3 people have the same birthday)+(probability that any 4 people have the same birthday)+(probability that any 5 people have the same birthday)
it is a bit like that but I am looking at five people with five different birthdays. I just want to know I am on the right track.

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not great with probability sorry, will get: @Mertsj @amistre64 @hartnn @Callisto @mathslover these guys are the beez neez
maybe they're not on right now, will try: @UnkleRhaukus and @hba pretty please?
was thinking now that the answer is 1-probability that 5 people have the same birthday...?
ok think I have worked it i.e. -1 1 person 365 2 364 3 363 4 362 and 5 361 do we mutiple all these with 365 days excluding a leap year? that is five people with five diffrent birthdays
ideas @hba ??
my idea is, and it could be faulty ...... \[\binom{5}{5}\left(\frac{1}{365}\right)^{5}\left(\frac{364}{365}\right)^{0}\]
ppppp ppppf pppfp ppfpp pfppp fpppp pppff ... i think the count for 5 people is 1+5+10+10+5+1 = 32 different scenarios
the probability that any given person has a birthday on a given day is 1/365, so the compliment of that is 364/365
...lol, never did like this particular one. satelitte has it tattoed someplace im sure
finding the chance that they have the same birthday might be easier; then its just 1-same birthdays

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