Question

Part 1: In two or more complete sentences, explain how to find the probability of being dealt three kings from a standard deck of 52 cards when three cards are dealt. In your final answer, include all necessary steps and calculations. Part 2: In two or more complete sentences, make a decision and support your position: Is Pascal's triangle an appropriate method to determine the probability in Part 1?

Answer 1

Part 1) The number of ways of dealing 3 cards from standrd deck without replacement (order important) is $3!\binom{52}{3}$ .

The number of ways of dealing 3 Kings without replacement (order important) is $3!\binom{4}{3}$ .

The required probability is

$\frac{3!\binom{4}{3}}{3!\binom{52}{3}}=\frac{\binom{4}{3}}{\binom{52}{3}}={\color{Blue} 0.000181}$

Part 2) Using Pascal's triangle we can find the values of Binomial coefficients.

$\binom{4}{3},\binom{52}{3}$ are binomial coefficients, and hence Pascal's triangle can be used for the calculation.

YES.