两道输血题

templars

1.At a dinner party, 5 people are to be seated around a circular table. Tow seating arrangement are considered different only when the position of the people are different relative to each other. What is the total number of different possible seating arrangement for the group?
A.5  B.10 C.24 D.32  E.120                                                  答案是C

2.For every positive even integer n, the function f(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
A. between 2 and 10      B. between 10 and 20   C. between 20 and 30  
D. between 30 and 40    E. greater than 40                      答案是E

都是prep 上的，不明白，大家帮帮忙吧，谢谢了

templars

非常感谢

shlshing

1.At a dinner party, 5 people are to be seated around a circular table. Tow seating arrangement are considered different only when the position of the people are different relative to each other. What is the total number of different possible seating arrangement for the group?
A.5  B.10 C.24 D.32  E.120                                                  答案是C

圓形排列，可視為直線排列少一項。這個例子中就取p（4,4)=4!  答案即26

2.For every positive even integer n, the function f(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
A. between 2 and 10      B. between 10 and 20   C. between 20 and 30  
D. between 30 and 40    E. greater than 40                      答案是E

由於F(100)=2*4*6*8*...*96*98*100 ，其中任何小於50的prime factor乘以二以後，都會成為一個小於一百的偶數，也就是f（100）的一個factor，舉例來說41是質數，但41＊2＝82，是f（100）的因數之一，故不可能是F(100)+1的因數，所以p必定大於50，選E