Although I gussed the right answer(D),I don't konw how to get it!Pls. help for it.Thanks a lot!
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.
当n是偶数的时候:
设n=2k,n(n+1)(n+2)=2k(2k+1)(2k+2)=4k(k+1)(2k+1)
注意k和k+1两者必有一个是偶数,所以4k(k+1)(2k+1)必定能被8整除。即满足条件的n有96/2=48个。
当n是奇数的时候:
注意到n(n+1)(n+2)中只有n+1是偶数,故只有当n+1能被8整除才能满足题目条件。n的取值可以是7,15,23……共 12个。
综上所述,n的取值一共有48+12=60个,概率是60/96=5/8。
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