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integers plus probability

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by atulmangal » Thu Jun 02, 2011 9:31 am
If two integers are chosen at random out of the set {2, 5, 7, 8}, what is the probability that their product will be of the form a2 - b2, where a and b are both positive integers?

A: 2/3
B: 1/2
C: 1/3
D: 1/4
E: 1/6
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by baladon99 » Thu Jun 02, 2011 9:39 am
B) 1/2 IMO Please confirm whether the ans is right .

I'm sorry the answer is A) 2/3 . But it took more than 3 mins for me :(
Last edited by baladon99 on Thu Jun 02, 2011 9:44 am, edited 1 time in total.
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by cans » Thu Jun 02, 2011 9:39 am
{2,5,7,8}
Total ways of selecting 2 numbers=6
2,5 - product = 10 can't be written as (a-b)(a+b)
2,7 - product=14 not possible
2,8 product = 16. (=4^2-0^2) but a,b need to be +ve integers thus not counted.
(=5^2-3^2) counted now.
5,7 product=35 = 6^2 - 1^2 counted
5,8 product=40 = 7^2 - 3^2 counted
7,8 product=56 = 9^2- 5^2 counted
Total = 4
Thus probability = 4/6 = 2/3
IMO A
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