/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 Find the value of each combinati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 20

Find the value of each combination. $$ { }_{9} C_{2} $$

Short Answer

Expert verified
The value of \[ { }_{9} C_{2} \]is 36.

Step by step solution

01

Understand the Combination Formula

The combination formula to find the number of ways to choose 'r' elements from a set of 'n' elements is given by \[ { }_{n} C_{r} = \frac{n!}{r!(n-r)!} \]
02

Substitute the Given Values

In the given problem, we need to find \[ { }_{9} C_{2} \]Here, \( n = 9 \) and \( r = 2 \). Substitute these values into the formula: \[ { }_{9} C_{2} = \frac{9!}{2!(9-2)!} \]
03

Simplify the Factorials

Simplify the factorial terms in the formula. Start by writing the factorials: \[ 9! = 9 \times 8 \times 7! \]Therefore: \[ { }_{9} C_{2} = \frac{9 \times 8 \times 7!}{2! \times 7!} \]
04

Cancel Common Factors

As you can see, \( 7! \) in the numerator and denominator cancel out: \[ { }_{9} C_{2} = \frac{9 \times 8}{2!} \]
05

Calculate the Remaining Terms

Now, calculate the value of \( 2! \): \[ 2! = 2 \times 1 = 2 \]Hence: \[ { }_{9} C_{2} = \frac{9 \times 8}{2} = \frac{72}{2} = 36 \]

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Factorials
Factorials are a foundational concept in combinatorics and various mathematical calculations. The factorial of a non-negative integer, denoted as \(!n\), is the product of all positive integers less than or equal to \(!n\). For example, \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]. Factorials are used in permutations, combinations, and other areas of mathematics. Understanding how to simplify and manipulate factorials can greatly assist in solving problems involving large numbers.
Let's consider more details:
  • \

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

What method of assigning probabilities to a simple event uses relative frequencies?

You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the table below. Do you think the die is loaded? Why? $$ \begin{array}{cc} \text { Value of Die } & \text { Frequency } \\ \hline 1 & 105 \\ \hline 2 & 47 \\ \hline 3 & 44 \\ \hline 4 & 49 \\ \hline 5 & 51 \\ \hline 6 & 104 \\ \hline \end{array} $$

According to Nate Silver, the probability of a senate candidate winning his/her election with a \(5 \%\) lead in an average of polls with a week until the election is \(0.89 .\) Interpret this probability.

What is the probability of an event that is impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean the event is impossible?

In seven-card stud poker, a player is dealt seven cards. The probability that the player is dealt two cards of the same value and five other cards of different value so that the player has a pair is \(0.44 .\) Explain what this probability means. If you play seven-card stud 100 times, will you be dealt a pair exactly 44 times? Why or why not?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.