Chapter 5: Q 5.162. (page 242)

Evaluate the following binomial coefficients.
$a . (\begin{matrix} 5 \\ 3 \end{matrix}) b . (\begin{matrix} 10 \\ 0 \end{matrix}) c . (\begin{matrix} 10 \\ 10 \end{matrix}) d . (\begin{matrix} 9 \\ 5 \end{matrix})$

Short Answer

Expert verified

Part (a) 10

Part (b) 1

Part (c) 1

Part (d) 126

Step by step solution

Part (a) Step 1. Given information.

The given binomial coefficient is:

$(\begin{matrix} 5 \\ 3 \end{matrix})$

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

$(\begin{matrix} 5 \\ 3 \end{matrix}) = \frac{5!}{3! \times (5 - 3)!} = \frac{5!}{3! \times 2!} = \frac{5 \times 4}{1 \times 2} = 10$

Part (b) Step 1. Evaluate the binomial coefficient 100.

$(\begin{matrix} 10 \\ 0 \end{matrix}) = \frac{10!}{0! \times (10 - 0)!} = \frac{10!}{0! \times 10!} = \frac{10!}{1 \times 10!} = 1$

Part (c) Step 1. Evaluate the binomial coefficient 1010.

$(\begin{matrix} 10 \\ 10 \end{matrix}) = \frac{10!}{10! \times (10 - 10)!} = \frac{10!}{10! \times 0!} = \frac{10!}{10! \times 1} = 1$

Part (d) Step 1. Evaluate the binomial coefficient 95.

$(\begin{matrix} 9 \\ 5 \end{matrix}) = \frac{9!}{5! \times (9 - 5)!} = \frac{9!}{5! \times 4!} = \frac{9 \times 8 \times 7 \times 6}{1 \times 2 \times 3 \times 4} = 126$

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Evaluate the following binomial coefficients.
$a . (\begin{matrix} 5 \\ 3 \end{matrix}) b . (\begin{matrix} 10 \\ 0 \end{matrix}) c . (\begin{matrix} 10 \\ 10 \end{matrix}) d . (\begin{matrix} 9 \\ 5 \end{matrix})$

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 100.

Part (c) Step 1. Evaluate the binomial coefficient 1010.

Part (d) Step 1. Evaluate the binomial coefficient 95.

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Evaluate the following binomial coefficients.a.53b.100c.1010d.95

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 100.

Part (c) Step 1. Evaluate the binomial coefficient 1010.

Part (d) Step 1. Evaluate the binomial coefficient 95.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Discrete Mathematics

Calculus

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Evaluate the following binomial coefficients.
$a . (\begin{matrix} 5 \\ 3 \end{matrix}) b . (\begin{matrix} 10 \\ 0 \end{matrix}) c . (\begin{matrix} 10 \\ 10 \end{matrix}) d . (\begin{matrix} 9 \\ 5 \end{matrix})$