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: `(14)/(45)` (2) `7/(55)` (3) `6/(55)` (4) `(12)/(55)`

Options

A. `(7)/(55)`
B. `(6)/(55)`
C. `(12)/(55)`
D. `(14)/(45)`

Answer

B

Explanation

We have, A `-=` {0, 1, 2, 3, 4, …, 10}
`n(S) = .^(11)C_(2)`
Let E be the given event.
`therefore E -=` {(0,4), (0,8),(2,6),(2,10),(4,8),(6,10)}
`therefore n(E) = 6`
`therefore P(E) = (6)/(55)`