• From: Jenny Wilkinson
  • Date: 15 Feb 1999
  • Subject: Probability of winning the Lottery

I read that the chance of winning the jackpot in the National Lottery is 1 in 14 million. Is this true? How is it calculated?

Maths Help suggests:

In the British National Lottery, six ball are selected at random from
forty-nine numbered balls. Players have to guess which six balls will
be drawn. If they get all six correct, they win the jackpot prize.

We need to work out the total number of possible ways of choosing six
different numbers from forty-nine.
Note that the order of choosing the numbers does not matter.
For example, the numbers 2 , 7 , 34 , 21 , 46 , 11
give the same winning combination as 34 , 11 , 7 , 21 , 2 , 46.

So the total number of possible ways of choosing six balls from forty-nine is

which is equal to
13 983 816
or approximately 14 000 000 (14 million).

Therefore, as you rightly said, the chance of a single ticket winning the
jackpot is approximately one-in-14million

USEFUL TIP: If your calculator has a button marked nCr
you can get the answer directly.
"n" stands for the total number (here n=49)
"r" stands for the number you want to select (here r=6)
So if you type in the sequence 49 nCr 6 =
you should get the result 13 983 816 directly.

nCr is shorthand for the number of different ways of choosing r items from n
where the order does not matter.

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