求助两道PREP数学题~~XDJM们帮帮忙

ack1111 · 发表于 2011-7-29 17:49:55

1. For every positive even integer n, the function h(n) is defined to be the product of all the even integers trom 2 to n. If p is smallest prime factor of h(100)+1, then p is greater than? 答案是大于40 这题不知道该用什么思路解。。。

2 A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is senior partner ?(The groups are consisdered different if at least one group member is different) 答案是100 为什么不是4*3*2+4*6*5+4*6*3

感谢大家了！！

ack1111 · 发表于 2011-7-29 18:40:17

没人来么

justgo · 发表于 2011-7-29 19:14:31

第一题写成2^50*50!+1则50以内的都不行；
第二题要考虑到重复计算，建议分情况逐步去写，不容易错。

bmwwhz · 发表于 2011-7-29 19:47:04

(1)h(100)+1=2的50次方*50！+1,也就是说除50以内的数都会有余数1，所以能除尽的数只能>50，p肯定就>50>40了。

(2)用全部情况减去分组里三个全是junior的情况就等于分组至少出现一个senior的情况。即10!/[3!*(10-7)!] - 6!/3!*(6-3)!=100

1. For every positive even integer n, the function h(n) is defined to be the product of all the even integers trom 2 to n. If p is smallest prime factor of h(100)+1, then p is greater than? 答案是大于40 这题不知道该用什么思路解。。。

2 A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is senior partner ?(The groups are consisdered different if at least one group member is different) 答案是100 为什么不是4*3*2+4*6*5+4*6*3

感谢大家了！！

-- by 会员 ack1111 (2011/7/29 17:49:55)

ack1111 · 发表于 2011-7-29 19:48:54

多谢大家~

求助两道PREP数学题~~XDJM们帮帮忙

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