I suggest this mapping: .

Of course is finite.

It is easy to show that is one to one.

Here are theorems that you need to do these sorts of cardinality problems.

There is an injection fromT1toAif and only if there is a surjection fromBtoB.A

If there is an injection fromT2toAthen the cardinality ofBat most the cardinality ofA.B

i.e. .

If there is an surjection fromT3toBthen the cardinality ofAat least the cardinality ofB.A

i.e. .