Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 12

Which of the following expressions is equivalent to \(\frac{12 !}{15 !} ?\) $$ \begin{aligned} & \text { } \frac{\frac{4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1}}{\frac{1}{15 \times 14 \times 13}} \\ & \frac{4}{5} \end{aligned} $$ I don't know.

Short Answer

Expert verified
None of the given options are equivalent to \( \frac{12!}{15 !} \). The simplified expression for \( \frac{12!}{15 !} \) is \( \frac{1}{15 \times 14 \times 13} \).

Step by step solution

01

Compare the factorials

We're looking at the expression \( \frac{12 !}{15 !} \). Since 12! is 12 x 11 x 10 x .... x 2 x 1 and 15! is 15 x 14 x 13 x 12 x 11 x 10 x...x 2 x 1, we see that 12! is a part of 15!.
02

Simplify the expressions

Since 12! is part of 15!, we can simplify by eliminating the common terms from the numerator and denominator of the expression as follows: \( \frac{12 !}{15 !} = \frac{1}{15 \times 14 \times 13} \).
03

Compare the given options

Comparing the obtained expression with the given options, it is clear that None of the given options are equivalent to \( \frac{12!}{15 !} \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Line 1 is defined by \(y=3 x+7\), and line 2 is perpendicular to line 1. What is the slope of line 2 ? \(\bigcirc-3\) O \(\frac{1}{3}\) \(\bigcirc-\frac{1}{3}\) O I don't know.

If \(x<0\), which of the following is true? \(O x^2\) is positive. \(x^2\) is negative. \(x^2\) could be either positive or negative. I don't know.

Which of the following is equivalent to \(x^{\frac{3}{2}}\) ? C \(\sqrt{x^3}\) \(\frac{3}{2} x\) \(\frac{x^2}{x^2}\) I don't know.

If \(0x^2 $$ \(x

If \(a, b\), and \(c\) are distinct prime numbers, how many factors does abc have?
See all solutions

Recommended explanations on English Textbooks

Lexis and Semantics

Read Explanation

English Grammar

Read Explanation

Email

Read Explanation

Synthesis Essay

Read Explanation

Language Acquisition

Read Explanation

Summary Text

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free