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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q 10. (page 836)

Evaluate $(\begin{matrix} 100 \\ 98 \end{matrix})$

Short Answer

Expert verified

The value of $(\begin{matrix} 100 \\ 98 \end{matrix}) = 4950$

Step by step solution

01

Step 1. Defination

if $j$ and $n$ are integers with $0 鈮� j 鈮� n$ , the symbol $(\begin{matrix} n \\ j \end{matrix})$ is defined as $(\begin{matrix} n \\ j \end{matrix}) = \frac{n!}{j! (n - j)!}$

02

Step 2. Explanation

$鈬� (\begin{matrix} 100 \\ 98 \end{matrix}) = \frac{100!}{98! (100 - 98)!}$

$鈬� (\begin{matrix} 100 \\ 98 \end{matrix}) = \frac{100 脳 99 脳 98 脳 97 鈰� 鈰� 脳 1}{(98 脳 97 脳 96 鈰� 鈰� 脳 1) (2 脳 1)}$

$鈬� (\begin{matrix} 100 \\ 98 \end{matrix}) = 4950$

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Most popular questions from this chapter

In Problems 61鈥�70, express each sum using summation notation.

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True or False. The notation $a_{5}$ represents the fifth term of a sequence.

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