Two numbers a and b are chosen at random from a set of first 30 natural numbers, then the probability that is divisible by 3 is

Explanation: CONCEPT: The number of combinations of n things taken r at a time is given by CALCULATIONS: Consider the first 30 natural numbers and the selection of two numbers 'a' and'b'could be selected as As is divisible by 3 If(a-b) is multiple of 3, then will be multiple of 3 also These numbers 135 If(a+b) is multiple of 3, then will be multiple of 3 also These numbers So total cases are Total numbers are 135+100=235 Required probability

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