Very confused with this Question, please help and explain: From a standard deck of cards, how many five card hands contain:

Question

From a standard deck of cards, how many five card hands contain:

c) 3 red cards and 2 clubs

Answer 1

There are 26 red cards in the deck, and 13 clubs.

That means there are ₂₆C₃ distinct red triplets, and ₁₃C₂ distinct club pairs. Multiplying those numbers gives the number of distinct 5-card hands fitting that description.

(Dividing that number by ₅₂C₅ gives the probability of being dealt such a hand, though the question does not ask for that.)