Two numbers `x and y` are chosen at random (without replacement) from among the numbers `1,2,3,...,2004.` The probability that `x^3+y^3` is divisible by `3` is (a) `1/3` (b) `2/3` (c) `1/6` (d) `1/4`

The integers x and y are chosen at random with replacement from nine natural numbers 1,2,3,….8,9 find the probability that (x^2-y^2) is divisible by 2

Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is

Two integers xa n dy are chosen with replacement out of the set {0,1,,2,3 ,.....10}dot Then find the probability that |x-y|> 5.

Three numbers are chosen at random without replacement from {1,2,3, …8}. The probability that their minimum is 3, given that their maximum is 6, is-

If two distinct numbers m and n are chosen at random form the set {1, 2, 3, …, 100}, then find the probability that 2^(m) + 2^(n) + 1 is divisible by 3.

Three numbers are chosen at random without replacement from {1,2,3,....10}. The probability that the minimum of the chosen number is 3 or their maximum is 7 , is:

Two number a and b are chosen at random from the set of first 30 natural numbers. Find the probability that a^2-b^2 is divisible by 3.

If two numbers a and b are-chosen at random from the 1st 30 natural numbers, find the probability that the expresion (a^2 -b^2) is divisible by 3.

Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}. Statement-1: The probability that the chosen numbers when arranged in some order will form an AP Is 1/(85) . Statement-2: If the four chosen numbers form an AP, then the set of all possible values of common difference is {1, 2, 3, 4, 5}. (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Two numbers are selected randomly from the set S={1,2,3,4,5,6} without replacement one by one. The probability that minimum of the two numbers is less than 4 is (a) 1/15 (b) 14/15 (c) 1/5 (d) 4/5