Evaluate the following. The notation ( n r ) means (n !)/(r !(n-r) !) . For example (

Name: Problem 51, Chapter 11: Intermediate Algebra
Uploaded: 2020-07-15T18:13:58-08:00
Duration: 35 s
Channel: Amy Jiang
Description: Evaluate the following. The notation ( n r ) means (n !)/(r !(n-r) !) . For example ( 5 3 )=(5 !)/(3 !(5-3) !)=(5 !)/(3 ! 2 !)=(5 ·4 ·3 ·2 ·1)/((3 ·2 ·1) ·(2 ·1))=10 ( 8 2 )

step 1 Okay, so we have 8 choose 2. This is the same as 8 factorial over 2 factorial, and an 8 minus 2,

Question

Evaluate the following. The notation $\left(\begin{array}{l}{n} \\ {r}\end{array}\right)$ means $\frac{n !}{r !(n-r) !} .$ For example $$\left(\begin{array}{l}{5} \\{3}\end{array}\right)=\frac{5 !}{3 !(5-3) !}=\frac{5 !}{3 ! 2 !}=\frac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(3 \cdot 2 \cdot 1) \cdot(2 \cdot 1)}=10$$ $$\left(\begin{array}{l}{8} \\{2}\end{array}\right)$$

   Evaluate the following.
The notation $\left(\begin{array}{l}{n} \\ {r}\end{array}\right)$ means $\frac{n !}{r !(n-r) !} .$ For example
$$\left(\begin{array}{l}{5} \\{3}\end{array}\right)=\frac{5 !}{3 !(5-3) !}=\frac{5 !}{3 ! 2 !}=\frac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(3 \cdot 2 \cdot 1) \cdot(2 \cdot 1)}=10$$
$$\left(\begin{array}{l}{8} \\{2}\end{array}\right)$$

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 11, Problem 51

Instant Answer

Solved by Expert Amy Jiang

07/15/2020

Step 1

Step 1: We are given $\left(\begin{array}{l}{8} \\{2}\end{array}\right)$ which means $\frac{8 !}{2 !(8-2) !}$. Show more…

Show all steps

Thanks for your feedback!

Evaluate the following. The notation $\left(\begin{array}{l}{n} \\ {r}\end{array}\right)$ means $\frac{n !}{r !(n-r) !} .$ For example $$\left(\begin{array}{l}{5} \\{3}\end{array}\right)=\frac{5 !}{3 !(5-3) !}=\frac{5 !}{3 ! 2 !}=\frac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(3 \cdot 2 \cdot 1) \cdot(2 \cdot 1)}=10$$ $$\left(\begin{array}{l}{8} \\{2}\end{array}\right)$$

Play audio

Feedback

Amy Jiang and 78 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Factorial

A factorial (n!) represents the product of all positive integers from 1 up to n. It is a fundamental concept in discrete mathematics and combinatorics, used to calculate the total number of ways to arrange n distinct objects.

Binomial Coefficient

The binomial coefficient, commonly expressed as 'n choose r' and calculated using the formula n!/(r!(n-r)!), determines the number of ways to choose r elements from a set of n elements without considering the order. It is crucial in the study of combinations and probability.

Combinatorics

Combinatorics is the branch of mathematics focused on counting, arrangement, and selection of elements within a set. Concepts like factorials and binomial coefficients are key tools in combinatorics, as they provide methods for calculating the number of possible configurations or selections in various scenarios.

Please give Ace some feedback