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If two different numbers are taken from the set `{0,1,2,3, ...... ,10};` then the probability that their sum as well absolute difference are both multiple of `4,` is: (1)`(14)/(45)` (2) `7/(55)` (3) `6/(55)` (4) `(12)/(55)`

A

`(7)/(55)`

B

`(6)/(55)`

C

`(12)/(55)`

D

`(14)/(45)`

Text Solution

AI Generated Solution

To solve the problem, we need to find the probability that the sum and the absolute difference of two different numbers selected from the set `{0, 1, 2, 3, ..., 10}` are both multiples of `4`. ### Step 1: Determine the Sample Space The set has 11 elements: `{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}`. We need to choose 2 different numbers from this set. The number of ways to choose 2 different numbers from 11 is given by the combination formula: \[ \text{Total ways} = \binom{11}{2} = \frac{11 \times 10}{2} = 55. ...
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