Question

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)` A. `(6)/(55)` B. `(12)/(55)` C. `(14)/(45)` D. `(7)/(55)` Select the correct answer from above options

Answer 1

Correct Answer - A Total number of ways of selecting 2 different numbers from {0,1,2,…..10}=^(11)C2=55 Let two numbers selected be x and y Then, x+y=4m …(i) and x-y=4n …(ii) ⇒2x=4(m+n)and2y=4(m+n) ⇒x=2(m+n)andy=2(m-n) ∴ x and y both even numbers ∴ Required probility = 6 55