If a single card is drawn from a standard 52-card deck, in how many ways could it be either a red...

Question:

If a single card is drawn from a standard 52-card deck, in how many ways could it be either a red card or a queen?

Use the general additive principle.

Additive Principle:

The additive principle of counting says, "if one thing can be done in {eq}m {/eq} ways and another thing can be done in {eq}n {/eq} ways and both the things can be done in {eq}p {/eq} ways, then either of the things can be done in {eq}m+n-p {/eq} ways.

Answer and Explanation:

In a standard deck of {eq}52 {/eq}-cards, there are {eq}26 {/eq} red cards, {eq}4 {/eq} queen cards and there are {eq}2 {/eq} red queen cards.

So we have:

$$m=26\\ n= 4\\ p=2 $$

By the additive principle of counting, the required number of ways is:

$$m+n-p= 26+4-2 = \color{blue}{\boxed{\mathbf{28}}} $$


Learn more about this topic:

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Solving Equations Using the Addition Principle

from Algebra I: High School

Chapter 8 / Lesson 11
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