Difference between revisions of "2000 SMT/Advanced Topics Problems/Problem 4"
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The possibilities for the numbers are: | The possibilities for the numbers are: |
Latest revision as of 09:40, 24 July 2020
Problem
Five positive integers from to
are chosen without replacement. What is the probability that their
sum is divisible by
SMT Solution
The possibilities for the numbers are:
all five are divisible bythree are divisible by
one is
and one is
two are divisible by
and the other three are either
or
one is divisible by
two are
and two are
four are
and one is
four are
and one is
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This gives us possible combinations out of
or
. So, the probability is
Credit
Problem and solution were taken from https://sumo.stanford.edu/old/smt/2000/