Combinations of Numbers

by Raabi Anony
(Karachi, Pakistan)

Hello everybody

It is my very first posting and hope receiving help and guidance from the Math Geeks. Here is my very 1st problem:

I have 2 equal sets of numbers 1 to 6 as below:

A = {1, 2, 3, 4, 5, 6}
B = {1, 2, 3, 4, 5, 6}

How many unique pairs of numbers can be made out of these 2 sets, like;
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
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(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

While manually doing, I get total number of 36 pairs and after deducting the repetitions, I get 32 pairs. But, by using the Combination Formula 12C2 (12 numbers taken 2 at a time), I get 66 pairs. Where am I wrong!
Actually, I want to solve this problem for a larger number of sets, like 10. I will appreciate clearing my confusions and suggesting the better algorithm, if any.

Please note that I am interested in the number of pairs only, just for a general purpose, without getting into any definition of Sets or the Ordered Pairs etc.

Thanks in anticipation.

Raabi