## whatu 2 years ago 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?

1. Jack1

= 1 - probability that 2 people have the same birthday

2. Jack1

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)

3. whatu

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.

4. Jack1

not great with probability sorry, will get: @Mertsj @amistre64 @hartnn @Callisto @mathslover these guys are the beez neez

5. Jack1

maybe they're not on right now, will try: @UnkleRhaukus and @hba pretty please?

6. Jack1

was thinking now that the answer is 1-probability that 5 people have the same birthday...?

7. whatu

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

8. Jack1

ideas @hba ??

9. amistre64

my idea is, and it could be faulty ...... $\binom{5}{5}\left(\frac{1}{365}\right)^{5}\left(\frac{364}{365}\right)^{0}$

10. amistre64

ppppp ppppf pppfp ppfpp pfppp fpppp pppff ... i think the count for 5 people is 1+5+10+10+5+1 = 32 different scenarios

11. amistre64

the probability that any given person has a birthday on a given day is 1/365, so the compliment of that is 364/365

12. amistre64

...lol, never did like this particular one. satelitte has it tattoed someplace im sure

13. amistre64

finding the chance that they have the same birthday might be easier; then its just 1-same birthdays