IIT JEE , AIEEE Forum - Mathematics , Algebra - (1) If a, b, c are natural no. than find out the probability of a2+b2+c2 is divisible by 7

hsbhatt

Sorry if I am bugging you, but I thought I should clarify this a bit

To take the point further, find the prob of the remainder being 1.

The favourable cases are permutations of (0,0,1) ; (0,4,4) and (2,2,4).

Case 1 occurs 3*2 = 6 times
Case 2 occurs 3*2*2 = 12 times
Case 3 occurs 3*2*2*2 = 24 times

Total = 42.

The prob = 42/343.

So, the remainders though being (0,1,..,6) they are all not equally likely

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