I\'m just learning probability and statistic stuff for thefirst time and I\'m a

Question

I'm just learning probability and statistic stuff for thefirst time and I'm a little confused on some things. Namley,when to use permutations, combinations, or just multiply. Iunderstand that permutations are for when order matters,combinations for when order doesn't matter, and multiplying forother things that I'm not quite sure of. The question I'm given says to find the probability of 10people having different birthdays. The total # of ways for 10people to have birthdays is 365^10. That part Iunderstand. For the total number of ways for 10 people tohave different birthdays I thought I would just do 365 C 10 becauseI'm choosing 10 different days out of 365. Then I'd justdivide 365 C 10 / 365^10. Is that correct? The answer I'm seeing does 365/365 * 364/365 *363/365 ...355/365. This to me looks like a permutation because itsn!/(n-k)! but permutation is for when order matters and it doesn'tseem to me like order matters in this case. I'm just learning probability and statistic stuff for thefirst time and I'm a little confused on some things. Namley,when to use permutations, combinations, or just multiply. Iunderstand that permutations are for when order matters,combinations for when order doesn't matter, and multiplying forother things that I'm not quite sure of. The question I'm given says to find the probability of 10people having different birthdays. The total # of ways for 10people to have birthdays is 365^10. That part Iunderstand. For the total number of ways for 10 people tohave different birthdays I thought I would just do 365 C 10 becauseI'm choosing 10 different days out of 365. Then I'd justdivide 365 C 10 / 365^10. Is that correct? The answer I'm seeing does 365/365 * 364/365 *363/365 ...355/365. This to me looks like a permutation because itsn!/(n-k)! but permutation is for when order matters and it doesn'tseem to me like order matters in this case.

Explanation / Answer

ok, this is basic multiplication think of it this way first person can have its birthday in any of the 365 days so365/365 second person can have its birthday in any of the 364 daysleft in order to make it different days, so 364/365 and so on for the 10 people, then just multiply thheir prob,that is why you get that answer

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