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probability

by ketkoag » Fri Apr 24, 2009 2:59 am
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

OA: D please explain how to solve it..
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by dmateer25 » Fri Apr 24, 2009 5:46 am
If n is an even it will be divisible by 8.

For example: 2 x 3 x 4 (has 2^3 in it, so it is divisible by 8)
4x5x6 (has 2^3 in it, so it is divisible by 8)


so that gives us 48 that are divisible by 8.

Now you have to look at when n is an odd number. When n is odd and the n+1 is divisible by 8, then these will be divisible by 8 as well.


so for example... 7 x8 x9..... 15x16x17.. These will all be divisible by 8 as well.

96/8 = 12


(48+12)/96 = 60/96 = 5/8
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