Yet another Lottery question.

Hagar · 04-08-2009, 20:34

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 · 04-08-2009, 20:47

$\displaystyle \left({{6}\choose{5}} \times \$1483\right) \left({{6}\choose{4}} \times \$46 \right) \left({{6}\choose{3}} \times \$5\right) = \$9688$

I couldn't get a Euro symbol

Pherekydes · 04-08-2009, 22:57

They are combinations, not permutations.

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

Yakuza · 05-08-2009, 13:27

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 · 05-08-2009, 15:00

Quote:

Originally Posted by Pherekydes

They are combinations, not permutations.

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

**Mellor** · 06-08-2009, 02:58

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 · 06-08-2009, 09:19

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

04-08-2009, 20:34	#1
Hagar Hosted Moderator Join Date: Apr 2002 Posts: 15,461 Adverts \| Friends HMod: RaN	Yet another Lottery question. 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. __________________

04-08-2009, 20:47	#2
red_fox Registered User Join Date: Jan 2006 Posts: 468 Adverts \| Friends	$\displaystyle \left({{6}\choose{5}} \times \$1483\right) \left({{6}\choose{4}} \times \$46 \right) \left({{6}\choose{3}} \times \$5\right) = \$9688$ I couldn't get a Euro symbol __________________ People said I was dumb, but I proved them!

04-08-2009, 22:57	#3
Pherekydes Registered User Join Date: May 2003 Location: Lucan Posts: 5,762 Adverts \| Friends	They are combinations, not permutations. And Alt Gr + 4 will give you € on a windows KB. (UK, of course) __________________ Boards Chess League Standings "But the stranger that dwelleth with you shall be unto you as one born among you, and thou shalt love him as thyself" Leviticus 19.34 "People are all the same, except when they are different." Abdullahi el-Tom

06-08-2009, 02:58	#6
Mellor Moderator Join Date: May 2006 Location: Bondi... Posts: 10,013 Adverts \| Friends Mod: Construction & Planning	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 __________________ Moneybookers is >>>>>> Neteller, Fact

06-08-2009, 09:19	#7
Hagar Hosted Moderator Join Date: Apr 2002 Posts: 15,461 Adverts \| Friends HMod: RaN	Very clear explanation. Takes the mystery out of it, thanks very much. __________________

05-08-2009, 13:27	#4
Yakuza Registered User Join Date: Nov 1999 Location: Dublin Posts: 634 Adverts \| Friends	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 )

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