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

[being_doug]

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.

 

[Tide]

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?