Yet another Lottery question.

Hagar

Suppose I was the winner with last Saturday, my six numbers would have netted me a cool €6,974,582. "Lucky you" I hear you chorus but how much didn't I win?

The Lottery only pays out the biggest win but in theory I could have had many 5 number, 4 number and 3 number winning permutations.

How many "winning" permutations do I miss out on? And what would it have been worth?

5 numbers paid € 1,483
4 numbers paid € 46
3 numbers paid € 5

Thanks.

red_fox

[LATEX]\displaystyle \left({{6}\choose{5}} \times \$1483\right) + \left({{6}\choose{4}} \times \$46 \right)+ \left({{6}\choose{3}} \times \$5\right) = \$9688 [/LATEX]

I couldn't get a Euro symbol

Pherekydes

They are combinations, not permutations.

And Alt Gr + 4 will give you € on a windows KB. (UK, of course)

Yakuza

The way I remember the difference between permuatations and combinations is: for Permutations, Position is important (and combinations is the other one!).

OP: in your question, position was not important, so it's the combinations you need (as Pherkedes pointed out), not permutations (although in English the two terms tend to be used interchangeably).

Interestingly, what we call a combination lock should actually be called a permutation lock as position is important (4567 will open it but 4657 will not even though they are the same combination )

Hagar

Pherekydes wrote: »

They are combinations, not permutations.

Please excuse my ignorance, I am only one of the great unwashed masses.

Mellor

Its easy enough to work out in your head, without knowing the proper (shortest/quickest/technical) way to do it on a calc

No. of match 5s is easy. Every set of 5 leaves out one number. so its just how many times you can leave out a number, which is 6.

Match fours is leaving out 2, so its (6x5)/2=15
We divide by two as the order doesn't matter, as pointed out above

Match 3s is (6x5x4)/(3x2)=20

5 numbers paid € 1,483 x6 = 8898
4 numbers paid € 46 x15 = €690
3 numbers paid € 5 x20 = €100

total=€9688

Hagar

Very clear explanation. Takes the mystery out of it, thanks very much.