中六合彩頭獎的機會率

2007-05-30 10:11 pm
有冇人可以幫我計出中六合彩頭獎的機會率, 我記得阿sir 以前講過,但是不記得,應該要用combination的式去計.我想知道真正的答案(最好列埋算式).Thanks!

回答 (4)

2013-08-22 6:22 am
究竟是1/10,068,347,520定1 /13,983,816?
2007-06-01 1:01 am
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。
參考: 自己
2007-05-30 11:36 pm
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.
2007-05-30 11:15 pm
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。


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