GWD8数学求解

rabbit861013

Q7:

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department.  If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

 

A.     42

B.     70

C.     140

D.     165

E.      315

Q9:

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.    

B.    

C.    

D.    

E.     

rabbit861013

没有大牛吗，请帮帮忙。。。

yoles

从7个候选人中选1人进入数学部，再从另外10人中选2个进入计算机科学部 If 没有候选人能够同时在这两个部门中都有资格。所以就是7*C(2,10)=315

若n为偶数，则n+2也为偶数，这样因子就有两个2了，又因为n和n+2里面肯定有一个4的倍数，所以n或者n+2肯定有一个里面是4的倍数，则因子中有3个2了。所以若n为偶数时，n*（n+1）*（n+2）必然能被8整除。这样的n有2,4,6,..96.一共是48个.

若n为奇数，则n+2也是奇数，则要求n+1为8的倍数，n=7,15....95. 这样的n一共有12个。

60/96=5/8

rabbit861013

谢谢，原来是这样