/*! 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 7 Evaluate the given binomial coef... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 7

Evaluate the given binomial coefficient. $$\left(\begin{array}{c}100 \\\2\end{array}\right)$$

Short Answer

Expert verified
The value of the binomial coefficient \( \left(\begin{array}{c}100 \2\end{array}\right) \) is 4950.

Step by step solution

01

Understand the Problem

This exercise involves working out the binomial coefficient \( \left(\begin{array}{c}100 \2\end{array}\right) \). The formula for evaluating a binomial coefficient \( \left(\begin{array}{c}n \k\end{array}\right) \) is \( \frac{n!}{k!(n-k)!} \), where '!' denotes factorial.
02

Plug in the Values Into the Formula

Replace n with 100 and k with 2 in the formula to get \( \frac{100!}{2!(100-2)!} \).
03

Calculate Factorials and Simplify

Calculate that 2!=2 and (100-2)!=98!. The expression then becomes \( \frac{100!}{2!*98!} \). Since 100! is 100*99*98!, the expression can be further simplified by cancelling out 98! to obtain \( \frac{100*99}{2} \).
04

Final Computation

The final computation yields \( \frac{100*99}{2} = 4950 \).

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!

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

Rationalize the denominator: \(\frac{6}{\sqrt{3}-\sqrt{5}}\).

Will help you prepare for the material covered in the next section. Use the formula \(a_{n}=a_{1} 3^{n-1}\) to find the 7 th term of the sequence \(11,33,99,297, \dots\)

If \(f(x)=x^{2}+2 x+3,\) find \(f(a+1)\) (Section \(8.1,\) Example 3 )

Solve for \(P: A=\frac{P t}{P+t}\)

Explain how to write terms of a sequence if the formula for the general term is given.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

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.