Chapter 5: Q 5.159. (page 242)

Evaluate the following binomial coefficients.
$a . (\begin{matrix} 5 \\ 2 \end{matrix}) b . (\begin{matrix} 7 \\ 4 \end{matrix}) c . (\begin{matrix} 10 \\ 3 \end{matrix}) d . (\begin{matrix} 12 \\ 5 \end{matrix})$

Short Answer

Expert verified

Part (a) 10

Part (b) 35

Part (c) 120

Part (d) 792

Step by step solution

Part (a) Step 1. Given information.

The given binomial coefficient is:

$(\begin{matrix} 5 \\ 2 \end{matrix})$

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

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

Part (b) Step 1. Evaluate the binomial coefficient 74.

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

Part (c) Step 1. Evaluate the binomial coefficient 103.

$(\begin{matrix} 10 \\ 3 \end{matrix}) = \frac{10!}{3! \times (10 - 3)!} = \frac{10!}{3! \times 7!} = \frac{10 \times 9 \times 8}{1 \times 2 \times 3} = 120$

Part (d) Step 1. Evaluate the binomial coefficient 125.

$(\begin{matrix} 12 \\ 5 \end{matrix}) = \frac{12!}{5! \times (12 - 5)!} = \frac{12!}{5! \times 7!} = \frac{12 \times 11 \times 10 \times 9 \times 8}{1 \times 2 \times 3 \times 4 \times 5} = 792$

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Evaluate the following binomial coefficients.
$a . (\begin{matrix} 5 \\ 2 \end{matrix}) b . (\begin{matrix} 7 \\ 4 \end{matrix}) c . (\begin{matrix} 10 \\ 3 \end{matrix}) d . (\begin{matrix} 12 \\ 5 \end{matrix})$

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 74.

Part (c) Step 1. Evaluate the binomial coefficient 103.

Part (d) Step 1. Evaluate the binomial coefficient 125.

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Evaluate the following binomial coefficients.a.52b.74c.103d.125

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 74.

Part (c) Step 1. Evaluate the binomial coefficient 103.

Part (d) Step 1. Evaluate the binomial coefficient 125.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Evaluate the following binomial coefficients.
$a . (\begin{matrix} 5 \\ 2 \end{matrix}) b . (\begin{matrix} 7 \\ 4 \end{matrix}) c . (\begin{matrix} 10 \\ 3 \end{matrix}) d . (\begin{matrix} 12 \\ 5 \end{matrix})$