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.