If two different numbers are taken from ...

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 `p/q` find `|p-q|`

`9`

`49`

`7`

`(7)/(55)`

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The correct Answer is:

Total number of ways of selecting 2 different numbers from {0,1,2,…..10}=`^(11)C_2=55`
Let two numbers selected be x and y
Then, `x + y = 4m " " …(i)`
and `x - y =4n " "…(ii)`
`rArr 2x=4(m+n) and 2y=4(m+n)`
`rArr x=2(m+n) and y=2(m-n)`
`therefore` x and y both even numbers

`therefore " Required probility "=6/(55)`

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