Lottery lines

[dembee]

Using ten numbers, how many different lines could I put on the lottery?  How is this calculated?   Thanks

[crofter]

The answer is 210 lines

The method uses the mathematical concept of "combinations" - here unordered six-tuples.

Writing 5! to mean 5x4x3x2x1, the answer is given by 10!/6!x4! = 10x9x8x7/4x3x2x1 = 10x3x7 = 210

[acw]

I'm rubbish at maths, but i just thought that there's anothe reason I don't understand your question.  Do you mean "If the possible lottery numbers were 1,2,3,4,5,6.7.8,9,10, and I chose any 6 numbers to make my line, how many combinations are there?" or, more likely "If a lottery line consists of ten numbers, and I can use the numbers 1 to 49 inclusive once in each line, how many different combinations are there?"?  I'm rubbish at maths, but 210 seems really low.

[dembee]

Sorry if I wasn't clear.  If I choose 10 of the 49 numbers, how many different lines could I make?

[crofter]

demdee, That's how I read your original question

acw, If the second part of you reply means ... imagine that we had to choose 10 numbers from 49 (instead of 6) then there would be 8,217,822,536 combinations (instead of the present 13,983,816)

[acw]

Crofter, as I say - am v.bad at maths.  The number in your most recent post are a lot bigger than 210.  Please could you explain that bit to me agian! :-)

[QmunkE]

The odds on any one ball being chosen are:

6/49 for the first
5/48 for the second
4/47 for the third

etc.

If you multiply the fractions together, you get the probability of you picking the right numbers. Do 1/ your answer, and you get the number of six-ball combinations (13,983,816)

[johnalex]

If anyone can tell me 39 numbers that will definitely NOT be called in next week's lottery, I will give them �50,000.  I will then stake �210 on all the remaining combinations and will be guaranteed the jackpot. I don't even mind sharing it with five other winners.  So Crofter is right, perm any 6 from 10 = 210 (10x9x8x7x6x5 divided by 6x5x4x3x2x1).  Bet you I can stop gambling . . .

[donslot]

As an aside, anybody with a spare �10 say on a Rollover draw of the MAIN Lotto, could do the following.

A]  Simply pick for yourself TEN number from 1-49.

B]  Then on a spare sheet of paper write the numbers; 1,2,3,4,5,6,7,8,9,10.

C]  Beneath B's numbers write down your selected numbers.

D]  Finally, refer to the matrix below, substituting all of YOUR numbers for each of the matrix numbers per line. You will end up with Ten Lottery lines of 6 selections - unique - overall to you.  Simply bet these IF you want to assure youself that any THREE of YOUR 10 numbers OVERALL will line up at least once & possibly 5 times.

A]   1 2 3 4 5 6

B]   1 2 3 4 5 7

C]   1 2 3 4 5 8

D]   1 2 3 4 5 9

E]   1 2 3 4 5 10

F]    1 6 7 8 9 10

G]   2 6 7 8 9 10

A]   3 6 7 8 9 10

B]   4 6 7 8 9 10

C]   5 6 7 8 9 10

[johnalex]

Thanx for the matrix Donslot  -  I'm going to try it.  Reminds me of Littlewoods 'Lit-Plans', so much cheaper than full perms and you feel like you're playing roulette at the same time!!