If two different numbers are taken from the set 0, 1, 2, 3, ........, 10; then the probabi…

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 :

Accepted Answer

Let A = {0, 1, 2, 3, 4, ......., 10}

Total number of ways of selecting 2 different numbers from A is

n (S) = 11C2 = 55, where 'S' denotes sample space

Let E be the given event

$$ \therefore $$ E = {(0, 4), (0, 8), (2, 6), (2, 10), (4, 8), (6, 10)}

$$ \Rightarrow $$ n (E) = 6

$$ \therefore $$ P(E) = $${{n\left( E \right)} \over {n\left( S \right)}}$$ = $${6 \over {55}}$$

Solutions · 1