maths question
2010-09-26 8:14 am
If someone play a games 5 times and get 60 mark total,what is the probabillity of him to get it mark if the highest mark of each time is 20 and the lowest mark is 0 .
回答 (2)
2010-09-27 3:58 pm
✔ 最佳答案
Expand (1+x+x^2+...+x^20)^5 and consider the coefficient of x^60.(1+x+x^2+...+x^20)^5
=(1-x^21)^5/(1-x)^5
=[1-5x^21+10x^42-10x^63+...]*[H(5,0)+H(5,1)x+H(5,2)x^2+...+H(5,k)x^k+...]
the coefficient of the term x^60
=1*H(5,60)-5*H(5,39)+10*H(5,18)
=635376-5*123410+10*7315
=91476
P=91476/21^5 (about 0.0224)
2010-09-27 17:55:36 補充：
the numbers of nonnegative integer solutions of x1+x2+...+xn=k is H(n,k)=C(n+k-1, k)
2010-09-27 6:57 pm
H(5,0)+H(5,1)x+H(5,2)x^2+...+H(5,k)x^k+...]咩係H(X,Y)
收錄日期: 2021-04-13 17:32:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100926000051KK00021