Question

what is the probablity at least 2 people have the same birthday in a group of 18 people

Answer 1

It is expressed as "1 - the probability that no two people have the same birthday":\[1 - \frac{ 365 \times 364 \times 363 \times ... \times 350 \times 349 \times 348 }{ 365^{18} }\]

Answer 2

do i tmes all those than divided by the bottom

Answer 3

Yes, then take that quotient and subtract it from 1.

Answer 4

You do know that the "..." means everything in between, don't you?

Answer 5

yes

Answer 6

So, you will have to multiply out 18 numbers for the numerator in that second term. Okay, just got your answer there.

Answer 7

You'll notice that the first number to be multiplied is 365 which cancels with one of the 365's in the denominator. but writing it this way highlights the selections of birthdays as being all separate from each other.

Answer 8

Try this, or compare answer to this\[\frac{ 365^{18}-\frac{ 365! }{ (365-18)! } }{ 365^{18} }\]

Answer 9

That's a nice compact way to describe the situation without having to resort to the ellipses. Yes, it gives the same answer and helps conceptually, but is harder to compute, practically speaking.

Answer 10

Because hand-held calculators, at least mine, is not going to handle factorials as high as 365!