Expressions Of Pj Problems
Kings And Aces

4 Aces, 4 Kings
You are given 4 aces and 4 kings from the standard deck of 52 cards as (above diagram). How many different pairs of cards, each pair consisting of one ace and one king, can you form from the aces and the kings?

The string: S7P6A64 (Multi-criteria - permutation);
The Math:
Pj Problem of Interest (PPI) is of type Grouping/Interaction.
Let us assign numbers to the identities of the aces and kings. In other words:
Let the king of diamond be 1, king of heart be 2, king of spade be 3 and king of club be 4.
Also let the ace of diamond be 5, ace of heart be 6, ace of spade be 7 and ace of club be 8.
Then the pairing are as follows: 15, 16, 17, 18, 25, 26, 27, 28, 35, 36, 37, 38, 45, 46, 47, 48.
Therefore there are 16 different ways to pair the aces and the kings given the constraint.
In general, given n groups, each of size m, the number of groups that can be formed such that each of the formed groups contains one member from each of the n groups, is mn.
Using this expression for the current problem, we have 42 = 16.

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