I have regular deck of playing cards and I want to find out how many color combinations there are in the deck. The cards fall into two categories: red and black. Here are the givens. Total $52$ items; $2$ distinct, repetition; $26$ black; $26$ red; Cards like $7$ of diamonds and king of hearts are red, while cards like the ace of spades and jack of clubs are black.
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$\begingroup$HINT
Just focus on one color (say, red), and think about the position of the 26 red cards in the deck (positions range from 1 to 52). That is, the red cards take up 26 of the 52 possible positions ... so how many sets of 26 numbers out of 1 through 52 are there?
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