If Josh has 5 different pairs of socks and 4 different pairs of shoes, how many different combinations could he wear? 08 O 10 20 18 25
The Correct Answer and Explanation is:
To find the number of different combinations Josh can wear, we need to multiply the number of sock combinations by the number of shoe combinations.
Step-by-step solution:
Josh has:
- 5 different pairs of socks
- 4 different pairs of shoes
Since we’re talking about pairs, each combination refers to one complete pair of socks and one complete pair of shoes. He chooses 1 pair of socks from 5, and 1 pair of shoes from 4.
Using the Fundamental Principle of Counting, the total number of combinations is: Total combinations=Number of sock pairs×Number of shoe pairs=5×4=20\text{Total combinations} = \text{Number of sock pairs} \times \text{Number of shoe pairs} = 5 \times 4 = 20
✅ Correct Answer: 20
Explanation:
This type of problem is a classic example of a combinatorics question, where we are asked to find the total number of outfit combinations Josh can make using different articles of clothing. The key here is understanding that we are combining independent choices: socks and shoes. Each pair of socks can be matched with any pair of shoes, regardless of their style, color, or type.
Let’s visualize:
Suppose the sock pairs are labeled S₁, S₂, S₃, S₄, S₅, and the shoe pairs are labeled H₁, H₂, H₃, H₄.
If Josh wears S₁, he has 4 options for shoes: H₁, H₂, H₃, H₄.
The same goes for S₂ through S₅. That’s 4 shoe options for each of the 5 sock options.
So, we calculate: 5 (sock pairs)×4 (shoe pairs)=20 combinations5 \text{ (sock pairs)} \times 4 \text{ (shoe pairs)} = 20 \text{ combinations}
This approach follows the multiplication principle, which states that if one event can happen in m ways and another independent event can happen in n ways, then the two events together can occur in m × n ways.
This is a foundational principle in mathematics that helps us calculate possibilities without listing every single combination manually.
So, with 5 sock choices and 4 shoe choices, Josh has 20 different ways to dress his feet!
