继续请教prep1的数学（48，73，75，77，94，96），排列组合题不会的比较多~~

?48.
                6225-!-item-!-187;#058&004914

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district.  What is the minimum possible population that the least populated district could have?

(A) 10,700

(B) 10,800

(C) 10,900

(D) 11,000

(E) 11,100

key：D

“no district is to have a population that is more than 10 percent greater than the population of any other district.” 中 10 percent 指的是谁的10%？

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 a senior partner?  (Two groups are considered different if at least one group member is different.)

(A) 48

(B) 100

(C) 120

(D) 288

(E) 600

key：B

我是这样做的： C₄¹ *C₆² + C₄²*C₆¹
                            + C₄³

^{分三种情况，一个高级两个低级，两个高级一个低级，三个都是高级； 然后把三种情况相加。为啥就不对呢？}

？77.       9031-!-item-!-187;#058&006222

At a dinner party, 5 people are to be seated around a circular table.  Two seating arrangements are considered different only when the positions of the people are different relative to each other.  What is the total number of different possible seating arrangements for the group?

(A) 5

(B) 10

(C) 24

(D) 32

(E) 120

key：C

与站成一排的区别？

？94.       10331-!-item-!-187;#058&007190

A company plans to assign identification numbers to its employees.  Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0.  How many different identification numbers are possible?

(A) 3,024

(B) 4,536

(C) 5,040

(D) 9,000

(E) 10,000

key：B 

?96.
                    10591-!-item-!-187;#058&007292

According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice.  How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

(A)  25

(B)  34

(C)  50

(D)  67

(E)  100

key：A

？73.       8845-!-item-!-187;#058&006119

A certain company has 18 equally qualified applicants for 4 open positions.  How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?

(A) 18

(B) 72

(C) 180

(D) 1,260

(E) 3,060

key：E

1、“no district is to have a population that is more than 10 percent greater than the population of any other district.”

也就是说把132,000分到11个地方后，人最多的地区的不能比人最少地区的人多10%～

2、楼主的式子没有列错，但是算错了～C₄¹ *C₆² =60   C₄²*C₆¹=36  C₄^{3 =} 4，加起来应该是100的～

这道用全集减不是容易些吗？总共10个选3个，减去全部J的情况 

3、直线与园的区别就是：圆的5个位置是相对的，也就是某一种排列 与 每个人向下轮一个位置得到的排列 是一种情况。

举例：直线中ABCDE与EABCD是两个不同排列，而圆中ABCDE与EABCD是同一种排列，因为相对位置没有变化。

圆中的公式就是直线的元素减去1个元素的全排列，这里是5个元素，在圆里排就是A44了。

4、题目中说要从0-9中4个不同的数字，第一位除0有9个数，第二位除了第一位选走的还有9个数，然后是8，7，答案就是9*9*8*7=4536

5、这题楼主看题不仔细，题目问用12-ounce cans 的浓缩去做6-ounce的果汁，所以你得到的答案就要在除以2了

6、最后一题，18人选4个...C18 4 就行了...

myjane,

could you please let me know where I could get Prep Math? Thanks a lot.

teethy

sure! you can follow the link below

http://forum.chasedream.com/dispbbs.asp?boardID=22&ID=350024&page=2

：）