A=(1,2,3.....30) How many 3 element subsets of A are there such that sum of its elements is divisible by 3?
Like (1,3,5) or (6,9,3)
Hello, kastamonu!
How many 3-element subsets of are there
such that sum of its elements is divisible by 3?
Consider the three subsets of
Set : multiples of 3.
. .
Set : one more than a multiple of 3.
. .
Set : one less than a multiple of 3.
. .
There are four ways to get 3 elements whose sum is a multiple of 3.
[1] 3 from ways. .*
[2] 3 from ways. .*
[3] 3 from ways. .*
[4] One from each subset: . ways. .*
Therefore: . ways.
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*
An explanation is available upon request.