# Suppose five cards are dealt at random from a well-shuffled 52-card deck. a. What is the...

## Question:

Suppose five cards are dealt at random from a well-shuffled 52-card deck.

a. What is the probability of getting four aces?

b. What is the probability of getting three aces and two kings?

## Probability:

Let {eq}X {/eq} be the set of all possible outcomes. Let {eq}A {/eq} be an outcome. Notice that {eq}A {/eq} is a subset of {eq}X {/eq}. If {eq}|X| {/eq} means the number of elements of the set {eq}X {/eq}, then the probability that {eq}A {/eq} occurs is {eq}\displaystyle P(A) = \frac{ |A| }{ |X| } {/eq}.

The number of ways to choose r items from a set of {eq}n {/eq} items is {eq}\displaystyle C(n,r) = \frac{n!}{r! \cdot (n-r)!} {/eq}.

## Answer and Explanation:

The number of ways to choose 5 cards from a well-shuffled 52 card deck is {eq}\displaystyle |X| = C(52,5) = \frac{52!}{47! \cdot 5!} =...

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#### Learn more about this topic: What is Probability in Math? - Definition & Overview

from High School Algebra I: Help and Review

Chapter 24 / Lesson 7
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