Two numbers x and y are chosen at random (without replacement) from amongst the numbers 1, 2, 3,……, 2004. The probability that (x3+y3) is divisible by 3 is pq (p and q are co-prime). Find the value of (p + q).
Let E1=1,4,7, ...... (n each) [3n = 2004]
E2=2,5,8, ...... (n each)
E3=3,6,9, ...... (n each)
x and y belong to choosing one from E1 and E2, or choosing two out of E3
so, required probability =nC1nC1+ nC23nC2=13
∴pq=13⇒p+q=4