Chapter 12: Q. 211E (page 1213)

In the following exercises, evaluate.
$(a) (\begin{array}{l} 7 \\ 1 \end{array}) (b) (\begin{array}{l} 4 \\ 4 \end{array}) (c) (\begin{array}{l} 3 \\ 0 \end{array}) (d) (\begin{array}{l} 10 \\ 8 \end{array})$

Short Answer

Expert verified

(a) $7$

(b) $1$

(d) $45$

Step by step solution

Part (a) Step 1 Given information

Evaluate $(\begin{array}{l} 7 \\ 1 \end{array})$

Part (a) Step 2 Solution

$\begin{array}{rcl} (\begin{array}{l} 7 \\ 1 \end{array}) & = & \frac{7!}{(7 - 1)! \cdot 1!} \\ = & 7 \end{array}$

Part (b) Step 1 Given information

Evaluate $(\begin{array}{l} 4 \\ 4 \end{array})$

Part (b) Step 2 Solution

$\begin{array}{rcl} (\begin{array}{l} 4 \\ 4 \end{array}) & = & \frac{4!}{(4 - 4)! \cdot 0!} \\ = & 1 \end{array}$

Part (c) Step 1 Given information

Evaluate $(\begin{array}{l} 3 \\ 0 \end{array})$

Part (c) Step 2 Solution

$\begin{array}{rcl} (\begin{array}{l} 3 \\ 0 \end{array}) & = & \frac{3!}{(3 - 0)! \cdot 0!} \\ = & 1 \end{array}$

Part (d) Step 1 Given information

Evaluate $(\begin{array}{l} 10 \\ 8 \end{array})$

Part (d) Step 2 Solution

$\begin{array}{rcl} (\begin{array}{l} 10 \\ 8 \end{array}) & = & \frac{10!}{(10 - 8)! \cdot 8!} \\ = & 45 \end{array}$

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In the following exercises, evaluate.
$(a) (\begin{array}{l} 7 \\ 1 \end{array}) (b) (\begin{array}{l} 4 \\ 4 \end{array}) (c) (\begin{array}{l} 3 \\ 0 \end{array}) (d) (\begin{array}{l} 10 \\ 8 \end{array})$

Short Answer

Step by step solution

Part (a) Step 1 Given information

Part (a) Step 2 Solution

Part (b) Step 1 Given information

Part (b) Step 2 Solution

Part (c) Step 1 Given information

Part (c) Step 2 Solution

Part (d) Step 1 Given information

Part (d) Step 2 Solution

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In the following exercises, evaluate.(a)71(b)44(c)30(d)108

Short Answer

Step by step solution

Part (a) Step 1 Given information

Part (a) Step 2 Solution

Part (b) Step 1 Given information

Part (b) Step 2 Solution

Part (c) Step 1 Given information

Part (c) Step 2 Solution

Part (d) Step 1 Given information

Part (d) Step 2 Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

In the following exercises, evaluate.
$(a) (\begin{array}{l} 7 \\ 1 \end{array}) (b) (\begin{array}{l} 4 \\ 4 \end{array}) (c) (\begin{array}{l} 3 \\ 0 \end{array}) (d) (\begin{array}{l} 10 \\ 8 \end{array})$