tryingtoexcelatmath
New member
- Joined
- Mar 5, 2018
- Messages
- 26
Question: What is the probability of 2 people having the same birthday in the room?
There are 50 people in the room, we are only looking at regular years, 365 days, not leap years.
Solution Provided: Using the subtraction principle: 1 - ((365 * 364 * ... * 316) / (365^50))
My Question: the numerator looks like it is using permutations nPr, but shouldn't the numerator be using combinations nCr?
If for example we only look at 3 people in the room, we could get Jan 1, 2020, Mar 1, 2020, and Dec 1, 2020.
But we only want people with different birthdays, so wouldn't that be the same as getting Dec 1, 2020 then Mar 1, 2020 then Jan 1, 2020?
To me it seems like order does not matter, thus shouldn't the top be nCr instead of nPr?
There are 50 people in the room, we are only looking at regular years, 365 days, not leap years.
Solution Provided: Using the subtraction principle: 1 - ((365 * 364 * ... * 316) / (365^50))
My Question: the numerator looks like it is using permutations nPr, but shouldn't the numerator be using combinations nCr?
If for example we only look at 3 people in the room, we could get Jan 1, 2020, Mar 1, 2020, and Dec 1, 2020.
But we only want people with different birthdays, so wouldn't that be the same as getting Dec 1, 2020 then Mar 1, 2020 then Jan 1, 2020?
To me it seems like order does not matter, thus shouldn't the top be nCr instead of nPr?