Maths problems - advice please

[Pie]

How To Calculate UK National Lottery Odds (Stolen word for word - I'm crap at maths)



The Jackpot
Winning Ticket Requirement: 6 numbers have to match the 6 main balls drawn

Note that the bonus ball is not taken into account, although it is represented for referential purposes



This calculation proves that the odds of winning the UK National Lottery jackpot are 1 in 13,983,816

[Pie]

Shouldn't it be 49 o the power of 6?
I make that 13.8 billion.

I think that's true if you had to match the actual sequence the balls are drawn to the sequence you picked them on your ticket.
Thankfully for the UK lottery it's any order - otherwise the jackpot may well be up to the billions by now!

[MikeFish]

Yes, good point Pie.

[Pyrotechnic]

The originals are:

Meals: 4x4x4 or 4^3 or 64 combinations
Cars: 5x5x5x5 or 5^4 or 625 combinations

For all the lottery it would be 49! ('49 factorial') or 49x48x47...3x2x1 or 6.082818640342679x10^62 combinations, but we only need 6 balls, so it's 49x48x47x46x45x44 or 10,068,347,520 to 1

[adsgreen]

The originals are:

Meals: 4x4x4 or 4^3 or 64 combinations
Cars: 5x5x5x5 or 5^4 or 625 combinations

For all the lottery it would be 49! ('49 factorial') or 49x48x47...3x2x1 or 6.082818640342679x10^62 combinations, but we only need 6 balls, so it's 49x48x47x46x45x44 or 10,068,347,520 to 1

Not correct - as above the order doesn't matter.
So the permutation 1-2-3-4-5-6 is equivalent to 6-5-4-3-2-1.

As such you need to take the number of permutations that are equivalent to arrive at the correct number of combinations.
So how many? Simple - its the number of permutations you can arrange 6 numbers.
This is 6! or 6x5x4x3x2x1 which gives the correct answer of approx 13million to 1.

[Pyrotechnic]

The originals are:

Meals: 4x4x4 or 4^3 or 64 combinations
Cars: 5x5x5x5 or 5^4 or 625 combinations

For all the lottery it would be 49! ('49 factorial') or 49x48x47...3x2x1 or 6.082818640342679x10^62 combinations, but we only need 6 balls, so it's 49x48x47x46x45x44 or 10,068,347,520 to 1

Not correct - as above the order doesn't matter.
So the permutation 1-2-3-4-5-6 is equivalent to 6-5-4-3-2-1.

As such you need to take the number of permutations that are equivalent to arrive at the correct number of combinations.
So how many? Simple - its the number of permutations you can arrange 6 numbers.
This is 6! or 6x5x4x3x2x1 which gives the correct answer of approx 13million to 1.

Close ;] 6! is 720, to get to the correct answer, which is, as you stated approx 13m (nearer 13.9m), you need to combine the 2, so it's 49!/6!

So, technically speaking, if you could guarantee to win more than £14m (far from impossible) you could buy every combination of ticket for £14m and come out in profit. Anyone want to lend me £14m...? (I think that's how it'd work anyway...)

[swannny]

eeeerm, how dare you!!

i was quite happily sitting here with a cold beer watching the footy, happily going brain dead, and then clicked on this topic.

my brain is now back in overload!

still, £14million..i'm game!