Quick maths check

[Basil]

Our village lottery is, pick three numbers between 1 and 25.
I'm saying the chances of winning are 1 in 13800.
Chaps in the pub insist the odds are much better than that,  but can't be specific.
Am I wrong?

[telstarbox]

Oops

[fuaran]

Assuming the order you pick your numbers doesn't matter? So you have to calculate the number of combinations, not permutations.
Number of combinations = n!/(k!*(n-k)!)

So for your lottery combinations = 25!/(3!*22!) = 2300

[JennyB]

Our village lottery is, pick three numbers between 1 and 25.
I'm saying the chances of winning are 1 in 13800.
Chaps in the pub insist the odds are much better than that,  but can't be specific.
Am I wrong?

I think you may be wrong. 1 in 13800  is the chance of picking the three balls in the same order (1/25×1/24×1/23)..
If the order doesn't matter, these you have three chances with the first  ball out, and two with the second, so the odds are six times better.

[Basil]

Thanks both.  I can see the error in my 25x24x23.  Not sure I understand how to work it out though. 

[αdαmsκι]

I agree with fuaran.

Here's my thinking.

You pick three numbers, say 10, 14 & 18.

In order to win the three numbers that are drawn need to be 10, 14 and 18 but the order doesn't matter.  The first number drawn could be 18, the second could be 10 and the third could be 14 and you still win.

The chance of 10 being drawn is 3/25 (as it could be the 1st, 2nd or 3rd number drawn)
The chance of 14 being drawn is 2/24 (we've already accounted for 10 being drawn, so we've only got 2 chances left and it's /24 because one number has already been drawn)
The chance of 18 being drawn is 1/23 (we've already accounted for 10 & 14 being drawn, so only 1 chance left and it's /23 because two numbers have already been drawn)

(3/25) * (2/24) * (1/23) = 1/2300

[Jaded]

Alternatively, Basil was a bit right, there are 13,800 combinations.

However there are 6 ways of getting the three numbers as they can be drawn in any order.

10, 14, 18
10, 18, 14
14, 10, 18
14, 18, 14
18, 10, 14
18, 14, 10

So the overall odds of winning are 6/13,800

Which is 1/2,300