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Question

# If two different numbers are taken from the set {0,1,2,3,⋯,10}; then the probability that their sum as well as absolute difference are both multiple of 4, is:

A
655
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B
1255
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C
1445
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D
755
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Solution

## The correct option is A 655 From the given conditions, x1+x2=4α and x1−x2=±4β Solving the two equations, we get x1=2(α±β) i.e, x1 is multiple of 2. x1x204,826,1040,862,1080,4102,6 ​​​​There are total 12 possibilities. Since (x1,x2) and (x2,x1) are same in this case, there is only 6 possibilities. Hence, required probability =611C2=655

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