Multivariate Hypergeometric Probability

I want to determine the probability of drawing specific cards from a deck using Hypergeometric Probability. In this case however, the cards will be drawn from multiple pools and the hand drawn will have multiple requirements. Below is an example.

Using a standard 52 card deck, a hand of 5 cards is drawn. What is the possibility of drawing 2 clubs and 1 heart in the 5 card hand.

Please note that while I am good with maths/physics, I am a statistics novice, so please provide me with the an appropiate method I can use with little prior knowledge.