It's versus and
Consider 2 numbers and which are chosen at random from the set without replacement . If the probablity that is divisible by 3 can be written of the form
where and , find
If you feel that the probability cannot be expressed in this form then type 22 as your answer.
The answer is 0.
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1 solution
The entire set can be split up into 3 sets of numbers of the form 3 m + 1 , 3 m + 2 , 3 m ,Three numbers can be chosen in ( 2 3 n ) ways. Also for sum of the cubes of the nos. To be divisivle by three either the numbers must be chosen from the third set o r one from set1 a n d the other from set 2. This can be done in ( 1 n ) 2 + ( 2 n ) ways. Therefore the required probability is ( 2 3 n ) ( 1 n ) 2 + ( 2 n ) which simplifies to 1/3. Comparing we get a=0, b=0 and c=1. Hence the answer is 0.