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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 309 (page 1220)

In the following exercises, evaluate.
a. $(\begin{array}{l} 1 \\ 1 \end{array})$
b. $(\begin{array}{l} 15 \\ 15 \end{array})$
c. $(\begin{array}{l} 4 \\ 0 \end{array})$
d. $(\begin{array}{l} 11 \\ 2 \end{array})$

Short Answer

Expert verified

The value is $1, 1, 1, 55$ respectively

Step by step solution

01

Part (a) Step 1: Given information

Given the binomial coefficient $(\begin{array}{l} 1 \\ 1 \end{array})$

02

Part (a) Step 2: Calculate using the formula

Calculating, we get

$(\begin{array}{l} 1 \\ 1 \end{array}) = 1 (\begin{array}{l} 1 \\ 1 \end{array}) = 1$

03

Part (b) Step 1: Given information

Given the binomial coefficient $(\begin{array}{l} 15 \\ 15 \end{array})$

04

Part (b) Step 2: Calculate using the formula

Calculating, we get

$(\begin{array}{l} n \\ n \end{array}) = 1 (\begin{array}{l} 15 \\ 15 \end{array}) = 1$

05

Part (c) Step 1: Given information

Given the binomial coefficient $(\begin{array}{l} 4 \\ 0 \end{array})$

06

Part (c) Step 3: Calculate using the formula

Calculating, we get

$(\begin{array}{l} n \\ 0 \end{array}) = 1 (\begin{array}{l} 4 \\ 0 \end{array}) = 1$

07

Part (d) Step 1: Given information

Given binomial coefficient $(\begin{array}{l} 11 \\ 2 \end{array})$

08

Part (d) Step 2: Calculate using the formula

Calculating, we get

$(\begin{array}{l} n \\ r \end{array}) = \frac{n!}{r! (n - r)!} (\begin{array}{l} 11 \\ 2 \end{array}) = \frac{11!}{2! (11 - 2)!} (\begin{array}{l} 11 \\ 2 \end{array}) = \frac{11!}{2! 脳 9!} (\begin{array}{l} 11 \\ 2 \end{array}) = \frac{11 脳 10 脳 9!}{2! 脳 9!} (\begin{array}{l} 11 \\ 2 \end{array}) = 55$

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