中六合彩頭獎的機會率

究竟是1/10,068,347,520定1 /13,983,816?

好容易。
六合彩頭獎組合共有:
(49)C(6) (nCr)=13983816，所以機會率是1/13983816。

The probabity of the 1st draw ball : 6/49 (6 number out of 49 ball)
2nd :5/48 (5 number out of 48 ball, a number and a ball was chose)
and etc

so the probabity is (6 X 5 X 4 X 3 X 2 X 1) / (49 X 48 X 47 X 46 X 45 X 44)

By the use of combination

There are 49 C 6 combinations of mark6 (C is combination)

n C r = n! / r! / (n-r)!
where n! = n(n-1)(n-2)......(2)(1)
From defination 0! = 1, 1! = 1

The total combination of mark6 is 49!/43!/6!

=(49 X 48 X .....) / (43 X 42 .....) / (6 X 5...)
=(49 X 48 X 47 X 46 X 45 X 44) / (6 X 5 X 4 X 3 X 2 X 1)

The probabilty is 1/number of combination, that the same as the above.

2007-05-30 15:45:28 補充：
There is permutation, n P r = n! / (n-r)!.Mark6 asked for only combination but in US, the lottery asked for permutation, the probabity is much lower then our mark6 by r!. eg (6 X 5 X 4 X 3 X 2 X 1) = 720 if 6 balls are drew.

方法好簡單，就是
(1/49)*(1/48)*(1/47)*(1/46)*(1/45)*(1/44)
=1/10,068,347,520
即是100億6834萬7520份之一的機會。

2007-05-31 17:16:51 補充：
如果全港人人都買六合彩，平均每人買不同的一千多註，才一定中頭獎。