any Maths probability, odds whizz kids ?



Can anyone enlighten me please. My curiosity has the better of me and it's doing my "nut" in that i can't work the maths out for this !!

In the UK you have what's called HOTPICKS.

There are different option games for this - Pick 2 ,Pick 3, pick 4 and, Pick 5 with obviously different prize tiers.

 nb. the Pick 3 & Pick 4 is different to the US versions.

For all the above... you have to do as it says on the tin and get correct OUT OF 49 numbers !!!

Now, looking at say the odds of the HOTPICKS PICK 3 the odds have been given as getting this correct as a 1:922 chance.

Can anybody show me the maths for that calculation ?







Thoth's avatar - binary


I am assuming that the UK lotto is a 6 of 49 game and that your Pick 3 Hot Picks entails picking three specific numbers between 1 through 49 and matching them out of the six drawn by the lottery.

There is ((49!)/((49-6)!))/(6!)=13,983,816 ways to pick (or draw) six numbers from the pool of 49.  In case you didnt know, the exclamation mark in the formula above means Factorial in mathematics.

There is also ((49!)/((49-3)!))/(3!)=18,424 ways to choose or draw 3 numbers from 49.

Since there are 6 numbers being drawn from the pool, there are 20 different three digits combinations that can be made from those 6 (that is, without any regard to order, i.e. 1-7-29 is the same as 29-7-1) ((6!)/((6-3)!))/(3!)=20

Now, your odds of guessing 3 from 49 are 1 in 18,424, but since there are 20 different 3 digit combos drawn every game (made from the six balls drawn) then your odds are actually 18,424/20=921.2, which can be rounded up to 922.


Brilliant Thoth ! Thanks for explaining.


Yes the main National Lottery game in UK is a 6/49 game.

 My confusion about the odds was highlighted when i saw that for the different prize tiers in that game ......... for choosing 3 numbers correct OUT of the 6 MAIN numbers drawn the odds of doing that correct 1:57 chance (thereabouts).


in the HOTPICKS PIck 3 game cause you are trying to get 3 numbers correct OUT OF the whole series of 49 numbers..... the odds became 1:922

I was just puzzled about that second calculation...

Thanks again !

Lucky !!!!Smile

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