跪求大牛解答三题曼哈顿数学题..

lishi87

Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.
Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value.

What is the chance that Bill finds at least one pair of cards that have the same value?

A 8/33

B 62/165

C 17/33

D 103/165

E 25/33

lishi87

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

x = w
x > w
x/y is an integer
w/z is an integer
x/z is an integer

lishi87

A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

a) 5/6
b) 1/5
c) 1/6
d) 1/7
e) 1/24

YvonneJim

顶！第一题也是不会做！

sqsdwdza

第一题C吧

sqsdwdza

然后  是 C    D？ 自己做的  不知道对不对

lishi87

然后  是 C    D？ 自己做的  不知道对不对

-- by 会员 sqsdwdza (2011/12/17 16:02:29)

C C D对的...

sqsdwdza

第一题分情况讨论  1对 和 2对
1对中再分  取一对后剩下2个球是取1个SUIT 还是2个

第二题可以带数字直接试   C选项错误的推断：Y可以看成一个等差数列  X为等差数列和  A1，A1。。。A1+（Y-1）
 X=（2A1+Y-1)Y/2     X/Y=A1+（Y-1）/2   A1为常数  而 Y必为偶数（ y = 2z） 所以 X/Y不可能为整数

设每个UNITS有X个NON   总共SENSORS为Y
UP=Y-30X            （Y-30X）/5=x          可以算出X与Y的比例关系   最后代入（Y-30X）/Y