What is the Probability Each Player Receives One Black Card in a Card Game?

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The discussion centers on calculating the probability that each of four players receives one black card from a deck containing 4 black cards and 12 red cards. Participants seek guidance on setting up the problem and solving it, referencing a similar example from the Bertsekas/Tsitsiklis "Intro to Probability" book. Key questions include determining the total number of ways to deal four cards to four players and the specific arrangements that ensure each player receives exactly one black card. Understanding these combinations is crucial for solving the probability problem. The conversation emphasizes the need for clarity in the mathematical setup to arrive at the correct solution.
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Homework Statement


A well shuffled deck has 4 black cards and 12 red cards (16 total). The cards are
dealt out to 4 players (each gets 4 cards). What is the probability that each player will have 1 black card?

Homework Equations



Asking how to set this up and solve this.

The Attempt at a Solution



There's a solution in the Bertsekas/Tsitsiklis "Intro to Probability" book for a similar problem, but I don't understand the explanation.
 
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In how many ways can you deal four cards to four people from a deck of 16?

In how many ways can you deal four cards to four people from a deck of 16 such that each receives exactly one black card?
 

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