h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Me and some guys at work are doing 20 games to finish 3 - 3 . We have worked out that it is 190 doubles but are stumped as to how many trebles and fourfolds there are. Can anyone help us??????????????

We are going to do a 1p unit stake and with odds of 50 / 1 we will get £26 for a double and around £1400 if we get three up , we need to know how many threes there are though....................

I reckon there are 1140 possible trebles

1,2,3
1,2,4
1,2,5
etc to
1,2,20

That's 18 isn't it.

Then

1,3,4
1,3,5
etc. to
1,3,20

That's another 17.

And so on.

Until you get to

1,19,20.

But then you start with

2,3,4
2,3,5
2,3,6

In fact use the factorial! or the nCr button on your calculator.

Assuiming you have a Casio fx-901 or equivalent,
type
20
shift
nCr
3
=


The answer is 1140.

The same answer is obtained by 20!/(3! x (20-3)!).

By the same method, you'll find the number of quadruples is 4845.

Trout