Problem 30
Question
A popular brand of pen is available in three colors (red, green, or blue) and four writing tips (bold, medium, fine, or micro). How many different choices of pens do you have with this brand?
Step-by-Step Solution
Verified Answer
There are 12 different choices of pens with this brand.
1Step 1: Identify the number of choices for each category
First and foremost, identify how many choices are available for each category. In this case, there are 3 colors (red, green, blue) and 4 types of writing tips (bold, medium, fine, micro) for the pens.
2Step 2: Apply the counting principle
The counting principle states that if you can do one task in a number of ways and a second task in b number of ways, then both tasks can be done in a*b number of ways. This principle applies to this problem, where ‘a’ is the number of choices for pen color and ‘b’ is number of choices for pen tips.
3Step 3: Calculate the total number of pen choices
Now, calculate the total number of combinations using the counting principle. Multiply the number of color choices by the number of tip choices (3 pen colors * 4 pen tips).
Other exercises in this chapter
Problem 30
Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (a+2 b)^{6} $$
View solution Problem 30
find each indicated sum. $$ \sum_{i=1}^{6} 7 i $$
View solution Problem 30
Use mathematical induction to prove that each statement is true for every positive integer n. \(\sum_{i=1}^{n} 7 \cdot 8^{i}=8\left(8^{n}-1\right)\)
View solution Problem 30
Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for \(a_{n}\) to find \(a_
View solution