[原创]2006年10月jj讨论稿第1篇(1-91)

爱穿越太平洋

13. A three-digit code consists of digits from 0 to 9. If the first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot be 0 at the same time, how many codes are possible?

answer:

分开算，__/__/__  1，让第二个数字是0，8*1*9=72

 2，让第二个数字是1，8*1*10=80 

 所以，一共是152种可能

 14. A jar contains 12 balls, including three red and nine blue; another jar contains 20 balls, including eight red and 12 blue. If one ball is selected from each of the two bags, what is the probability that two blue balls will be selected?

answer: （9/12）*（12/20）=9/20

15. What is the remainder when positive integer x is divided by 7 1). X+1 is divisible by 7 2). X+13 is divisible by 7

answer: Answer: D   1, remainder is 6,

                   2, remainder is 1

16. A company has assigned a distinct 3-digit code number to each of its 330 employees. Each code number was formed from the digits 2, 3, 4, 5, 6, 7, 8, 9 and no digit appears more than once in any one code number. How many unassigned code numbers are there?

answer: P₈³-330=6

 17. K=wxyz, where w, x, y, z are prime numbers. Not including 1 and K, how many factors does K have?

answer:14. 因为不包含1 和K（K就是WXYZ），
                    所以，factors有4+C₄²+C₄³=14

             p.s. C₄²是两两因子相乘的因数，C₄³是三个因子相乘的因数

 18. Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?

answer:  20。

       X+Y=30

           （10X+20Y）/30=18

            推出：X=6 ，Y=24

           又有（10*6+20Z）/（6+Z）=14

　　　　　　推出：Z=4

　　　　　　故，24-4=20个2-pound的箱子要被移走

leebowl

 

11. 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?

讨论：P₃¹*P₅²+P₅⁵/p₃³=80  我的算法是这样，但是不敢确定~    大家来拍砖
能不能解释一下为什么这么算啊？
我是这样想的：如果不是圆桌，就按普通排序：5！
但是由于圆桌，每种排序就会有5种是一样的，比如这种排序：12345，在圆桌中它其实和51234，45123，34512，23451相同，大家围成一个圆相对位置其实没有变。同样每一种都有这种情况，
所以最后是5!/5=4!=24

蓝夕叶子

12楼滴，为什么是5!/5这种算法啊？

蓝夕叶子

11题米有思路。。。

今天第一次参加math讨论，第一个感想就是：完了

leebowl

晕啊，我不是都解释了么。。。。。
我也不知道这样算对不对。。。

蓝夕叶子

那为什么是除以5呢？是不是有什么公式？

大家不要笑偶啊

leebowl

12345，在圆桌中它其实和51234，45123，34512，23451
有5种是重复的啊。。。。

yaomao

同意楼上的，
也可以这样算：
先让一个人在位置上坐定，
其余4个人来坐剩下的位置：P₄⁴
因为排序和坐的位置没有关系，只和周围的人有关
所以答案就是P₄⁴

蓝夕叶子

哦哦。。

sinoversion

以下是引用yaomao在2006-10-8 13:01:00的发言：
同意楼上的，
也可以这样算：
先让一个人在位置上坐定，
其余4个人来坐剩下的位置：P₄⁴
因为排序和坐的位置没有关系，只和周围的人有关
所以答案就是P₄⁴

agree.