Hello, wopashui!

Believe it or not this is a Combination problem.

But you'll have see the explanation.

Find the number of different ordered triples

such that if:

. . a) must be nonnegetive integers.

Place 12 objects in a row, inserting a space before, after and between them.

. .

Place two "dividers" in any of the 13 spaces.

So that: . .represents:

. . and: . .represents:

If the dividers are placed in twodifferentspaces, there are: . ways.

If the dividers are placed in thesamespace, there are: ways.

Hence, there are: . ways to place the dividers.

Therefore, there are triples of nonnegative integers whose sum is 12.

b) must be positive integers.

Place 12 objects in a row, inserting a space between them.

. .

Choose 2 of the 11 spaces and insert "dividers".

So that: . .represents:

. . and: . .represents:

The dividers are placed in twodifferentspaces.

. . There are: . ways.

Therefore, there are ordered triples of positive integers whose sum is 12.