Chapter 5: Q 5.161. (page 242)

Evaluate the following binomial coefficients.
$a . (\begin{matrix} 4 \\ 1 \end{matrix}) b . (\begin{matrix} 6 \\ 2 \end{matrix}) c . (\begin{matrix} 8 \\ 3 \end{matrix}) d . (\begin{matrix} 9 \\ 6 \end{matrix})$

Short Answer

Expert verified

Part (a) 4

Part (b) 15

Part (c) 56

Part (d) 84

Step by step solution

Part (a) Step 1. Given information.

The given binomial coefficient is:

$(\begin{matrix} 4 \\ 1 \end{matrix})$

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

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

Part (b) Step 1. Evaluate the binomial coefficient 62.

$(\begin{matrix} 6 \\ 2 \end{matrix}) = \frac{6!}{2! \times (6 - 2)!} = \frac{6!}{2! \times 4!} = \frac{6 \times 5}{1 \times 2} = 15$

Part (c) Step 1. Evaluate the binomial coefficient 83.

$(\begin{matrix} 8 \\ 3 \end{matrix}) = \frac{8!}{3! \times (8 - 3)!} = \frac{8!}{3! \times 5!} = \frac{8 \times 7 \times 6}{1 \times 2 \times 3} = 56$

Part (d) Step 1. Evaluate the binomial coefficient 96.

$(\begin{matrix} 9 \\ 6 \end{matrix}) = \frac{9!}{6! \times (9 - 6)!} = \frac{9!}{6! \times 3!} = \frac{9 \times 8 \times 7}{1 \times 2 \times 3} = 84$

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Evaluate the following binomial coefficients.
$a . (\begin{matrix} 4 \\ 1 \end{matrix}) b . (\begin{matrix} 6 \\ 2 \end{matrix}) c . (\begin{matrix} 8 \\ 3 \end{matrix}) d . (\begin{matrix} 9 \\ 6 \end{matrix})$

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 62.

Part (c) Step 1. Evaluate the binomial coefficient 83.

Part (d) Step 1. Evaluate the binomial coefficient 96.

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Evaluate the following binomial coefficients.a.41b.62c.83d.96

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 62.

Part (c) Step 1. Evaluate the binomial coefficient 83.

Part (d) Step 1. Evaluate the binomial coefficient 96.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Evaluate the following binomial coefficients.
$a . (\begin{matrix} 4 \\ 1 \end{matrix}) b . (\begin{matrix} 6 \\ 2 \end{matrix}) c . (\begin{matrix} 8 \\ 3 \end{matrix}) d . (\begin{matrix} 9 \\ 6 \end{matrix})$