A Combinatorics Problem D;

2009-05-29 3:10 am

The final score of a table tennis game is 11 : 6. In how many ways can this total score be achieved?
SOLUTION: 8008

On the other hand,
Given 8 numbers 77889911, how many 8-digit numbers can be form?
SOLUTION: First we assume that the 8 digits are distinct so that the number of permutation is 8!.
As there are two ‘7’,two ‘8’, two ‘9’s and two ‘1’s, the answer is 8!/(2!2!2!2!) .

back to the first problem,

i assume that it's asking:
(WLOG)
WWWWWW ( win x 6) LLLLLLLLLLL ( lose x 11)

then the answer should be 17!/(11!6!) = 12376

but i'm wrong... (sigh)
is that i have misunderstood the question??

please help .__.

更新1:

前一? sorry that i don't know what you are talking about! *sigh*

更新2:

do u mean that the result of last round is fixed?

回答 (2)

myisland8132

2009-05-30 1:22 am

✔ 最佳答案

1 Consider two player A and B and A is the winner. The game sequence will be A A B A B A ... A (Since the last game should be won by A) So the number of combinations is
(17-1)C(11-1)=16C10=16!/10!6!=8008
2 8!/2!2!2!2!= (Since there are 2 1's,7's,8's,9's respectively)

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螞蟻雄兵

2009-05-29 3:38 am

11:6
前一10:6
so
16!/(10!^6!)
=16*15*14*13*12*11/(6*5*4*3*2)
=8008

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