作者s987692 (阿诚)
看板Grad-ProbAsk
标题Re: [问题] 离散请教
时间Thu Mar 19 22:09:36 2009
※ 引述《xshane831 (Shane)》之铭言：
: ※ 引述《loeooo (篮球狂)》之铭言：
: : 1. how many solutions are there to the equation X1+X2+X3+X4+X5=21,
: : where Xi, i=1,2,3,4,5 is a nonnegative integer such that 0<=Xi<=10
: : 求整数解个数跟求非负整数解个数一样吗? 求整数解我会
: : 但求非负要怎麽求阿?
: 这是用生成函数解法 每个X的生成函数(1+X^1+X^2+...+X^10)
: 五个就是(1+X^1+...+X^10)^5 最後求X^21的系数
: : 2. There are _________ consecutive 0s at the end of the binary expansion
: : of 70!
: : 3. there are ________4-digit decimal telephone numbers haviing one or
: : more repeated digits.
: : 4. if there are five possible grades, A,B,C,D,and F, the minimum number of
: : students required in a class to be sure that at least six will receive the
: : same grade is ________________.
2. 4=2^2 >有两个零 8=2^3 >>有三个零
70! = [70/2](取下限)+[70/2^2](取下限)+[70/2^3](取下限)+[70/2^4](取下限)+
[70/2^5](取下限)+[70/2^6](取下限)
3. C(4,2)*C(10,1)*9*8*7 + C(4,3)*C(10,1)*9 + C(4,4)*C(10,1)*1
这题我比较不确定它题意是什麽~
4. 据鸽笼 5*5+1 = 26 至少有一个奖有六人拿~
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