2021 April MIMC 10 Problems/Problem 14
James randomly choose an ordered pair which both
and
are elements in the set
,
and
are not necessarily distinct, and all of the equations:
are divisible by
. Find the probability that James can do so.
Solution
We can begin by converting all the elements in the set to Modular of . Then, we realize that all possible elements that can satisfy all the expressions to be divisible by
can only happen if
and
are both
(mod
. Since
and
are not necessarily distinct, we have
possible
. There are total of
possible
, therefore, the probability is $\frac{9}{25}=\boxed{\textbf{(A) \frac{1}{25}}}$ (Error compiling LaTeX. Unknown error_msg).