Chapter 5: Q 5.160. (page 242)

Evaluate the following binomial coefficients.
$a . (\begin{matrix} 3 \\ 2 \end{matrix}) b . (\begin{matrix} 6 \\ 0 \end{matrix}) c . (\begin{matrix} 6 \\ 6 \end{matrix}) d . (\begin{matrix} 7 \\ 3 \end{matrix})$

Short Answer

Expert verified

Part (a) 3

Part (b) 1

Part (c) 1

Part (d) 35

Step by step solution

Part (a) Step 1. Given information.

The given binomial coefficient is:

$(\begin{matrix} 3 \\ 2 \end{matrix})$

Part (a) Step 2. Evaluate the binomial coefficient.

$(\begin{matrix} 3 \\ 2 \end{matrix}) = \frac{3!}{2! \times (3 - 2)!} = \frac{3!}{2! \times 1!} = 3$

Part (b) Step 1. Evaluate the binomial coefficient 60.

$(\begin{matrix} 6 \\ 0 \end{matrix}) = \frac{6!}{0! \times (6 - 0)!} = \frac{6!}{0! \times 6!} = 1$

Part (c) Step 1. Evaluate the binomial coefficient 66.

$(\begin{matrix} 6 \\ 6 \end{matrix}) = \frac{6!}{6! \times (6 - 6)!} = \frac{6!}{6! \times 0!} = 1$

Part (d) Step 1. Evaluate the binomial coefficient 73.

$(\begin{matrix} 7 \\ 3 \end{matrix}) = \frac{7!}{3! \times (7 - 3)!} = \frac{7!}{3! \times 4!} = \frac{7 \times 6 \times 5}{1 \times 2 \times 3} = 35$

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Evaluate the following binomial coefficients.
$a . (\begin{matrix} 3 \\ 2 \end{matrix}) b . (\begin{matrix} 6 \\ 0 \end{matrix}) c . (\begin{matrix} 6 \\ 6 \end{matrix}) d . (\begin{matrix} 7 \\ 3 \end{matrix})$

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Evaluate the binomial coefficient.

Part (b) Step 1. Evaluate the binomial coefficient 60.

Part (c) Step 1. Evaluate the binomial coefficient 66.

Part (d) Step 1. Evaluate the binomial coefficient 73.

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Evaluate the following binomial coefficients.a.32b.60c.66d.73

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Evaluate the binomial coefficient.

Part (b) Step 1. Evaluate the binomial coefficient 60.

Part (c) Step 1. Evaluate the binomial coefficient 66.

Part (d) Step 1. Evaluate the binomial coefficient 73.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Applied Mathematics

Geometry

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Evaluate the following binomial coefficients.
$a . (\begin{matrix} 3 \\ 2 \end{matrix}) b . (\begin{matrix} 6 \\ 0 \end{matrix}) c . (\begin{matrix} 6 \\ 6 \end{matrix}) d . (\begin{matrix} 7 \\ 3 \end{matrix})$