帮忙看一下几道题！

1. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office.  In how many ways can the company assign 3 employees to 2 different offices?

A.    5

B.     6

C.     7

D.    8

E.     9

答案是：D

分情况:

1)如果两个OFFICE是其中一个空的,那么就是三个职员先都在一起,选一个OFFICE就行了,共两种(因为两个OFFICE可选)

2)如果是MORE THAN, 那么就是一个OFFICE 2 EMPLOYERS,另一个OFFICE 1 EMPLOYERS,即 C(3,2)*P(2,2)--先选出那两个一起的EMPLOYERS,再排列到两个OFFFICE

相加,得D

Q11:                            

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              ׀        ׀        ׀        ׀        ׀   

     
   The figure shown represents a board with 4 rows of pegs, and at the bottom of the board are 4 cells numbered 1 to 4.  Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening.  The ball then has the probability 1/2 of passing through the opening immediately to the left of that peg and probability 1/2 of passing through the opening immediately to the right.  What is the probability that when the ball passes through the first two pegs at the top it will end in Cell 2? 

A.    1/16

B.    1/8

C.    1/4

D.    3/8

E.    1/2

答案是：D

郁闷啊！图形贴过来就变形了，想必大家应该在GWD上见过这个图了吧！

自己画画可能更清楚.

首先落到第三层无论进不进去那CELL,都是1/2的三次方=1/8

然后一画图,有三条路径事实上可以到达那个CELL

3/8

Meg and Bob are among the 5 participants in a cycling race.  If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?

A.     24

B.      30

C.     60

D.     90

E.      120

答案是：C。

解这个题好象可以用高中学过的排列组合中的插空法，可惜忘了。知道的同志麻烦回复一下。谢谢！

P(5,5)*1/2

因为或者在前,或者在后,概率相等

有三条路径？？指点一下。

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A.1/4       B.3/8      C.1/2       D.5/8      E.3/4

答案是D。但我认为应该是C才对。大家的看法呢？？