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Chapter 11: Problem 65

Using 15 flavors of ice cream, how many cones with three different flavors can you create if it is important to you which flavor goes on the top, middle, and bottom?

Short Answer

Expert verified
The number of different ice cream cones that can be created is 2730.

Step by step solution

01

Understand the Problem

We are given 15 unique flavors of ice cream, and we want to find the permutations of these flavors on an ice cream cone with three different positions (top, middle, bottom). A permutation is an arrangement of objects where the order is important.
02

Use Permutation Formula

The formula for permutation is \(nPn = n! / (n - r)!\) where \(n\) is the total number of options, \(r\) is the number of selections made, and \(!\) denotes a factorial, meaning the product of all positive integers up to that number. Here, \(n = 15\) and \(r = 3\), as we are selecting 3 flavors out of 15 to place on the cone.
03

Evaluate the Expression

Substitute the values into the formula. Evaluate \(15P3 = 15! / (15 - 3)!\). This can be further simplified by cancelling out terms, leaving us with \(15 脳 14 脳 13\). Find the product of these numbers.

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Most popular questions from this chapter

In Exercises \(105-108\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If the \(n\) th term of a geometric sequence is \(a_{n}=3(0.5)^{n-1}\) the common ratio is \(\frac{1}{2}\)

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises \(71-76\). A job pays a salary of \(\$ 24,000\) the first year. During the next 19 years, the salary increases by \(5 \%\) each year. What is the total lifetime salary over the 20 -year period? Round to the nearest dollar,

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Use this information to solve Exercises \(47-48 .\) The mathematics department of a college has 8 male professors, 11 female professors, 14 male teaching assistants, and 7 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a male.

If you toss a fair coin six times, what is the probability of getting all heads?
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