It's been some time since I studied probability. So, forgive me if this seems like a very simple question to answer, but after trying to wrap my head around it for two days without any success, I'm confident that once I understand it, the rest will become very clear.(adsbygoogle = window.adsbygoogle || []).push({});

Let me start with what I know:

Given a well-shuffled deck, what is the probability that the first hand drawn will be a 21 (an ace and a ten-valued card [T,J,Q,K])?

I know that drawing an ace will occur (4/52) and a ten will occur (16/51). Since the ten could have been drawn first, the probability is 2*(4/52)*(16/51) = 0.4827.

First question: Technically, should the equation be written as 2! * (4/52) * (16/51) = 0.4827 (note the factorial)?

Secondly, is there a generic form that allows me to calculate the probability of drawing cards? For example, drawing three 5s? Three aces and a four?

Am I correct for three 5s to write (4/52)*(3/51)*(2/50)*3! and (4/52)*(3/51)*(2/50)*(4/49)*4! for the three aces and a four?

I'm trying to write an algorithm to gather probabilities of drawing cards. I was surprised at being able to solve a subset sum problem earlier yet these basic probability problems elude me. :-/

Thank you!

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# What is the probability of drawing cards from a deck?

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