Two different numbers are taken from the set {0,1,2,3,4,5,6,7,8,9,10}. The probability that their sum and absolute value of difference both are multiple of 4 is x55, then x equals
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Solution
Total number of ways, n(S)=11C2=55
Let set A={0,4,8} and set B={2,6,10}
If both the numbers are taken from either A or B, then we have the favourable cases
Number of favourable cases = (3C2+3C2)=6 ∴ Required probability =655=x55⇒x=6