Chapter 12: Q. 212E (page 1213)

In the following exercises, evaluate.
(a) $(\begin{array}{l} 3 \\ 1 \end{array})$ (b) $(\begin{array}{l} 9 \\ 9 \end{array})$ (c) $(\begin{array}{l} 7 \\ 0 \end{array})$ (d) $(\begin{array}{l} 5 \\ 3 \end{array})$

Short Answer

Expert verified

(a) $3$

(b) $1$

(d) $10$

Step by step solution

Part (a) Step 1 Given information

Evaluate $(\begin{array}{l} 3 \\ 1 \end{array})$

Part (a) Step 2 Solution

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

Part (b) Step 1 Given information

Evaluate $(\begin{array}{l} 9 \\ 9 \end{array})$

Part (b) Step 2 Solution

$\begin{array}{rcl} (\begin{array}{l} 9 \\ 9 \end{array}) & = & \frac{9!}{(9 - 9)! \cdot 9!} \\ = & 1 \end{array}$

Part (c) Step 1 Given information

Evaluate $(\begin{array}{l} 7 \\ 0 \end{array})$

Part (c) Step 2 Solution

$\begin{array}{rcl} (\begin{array}{l} 7 \\ 0 \end{array}) & = & \frac{7!}{(7 - 0)! \cdot 0!} \\ = & 1 \end{array}$

Part (d) Step 1 Given information

Evaluate $(\begin{array}{l} 5 \\ 3 \end{array})$

Part (d) Step 2 Solution

$\begin{array}{rcl} (\begin{array}{l} 5 \\ 3 \end{array}) & = & \frac{5!}{(5 - 3)! \cdot 3!} \\ = & 10 \end{array}$

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In the following exercises, evaluate.
(a) $(\begin{array}{l} 3 \\ 1 \end{array})$ (b) $(\begin{array}{l} 9 \\ 9 \end{array})$ (c) $(\begin{array}{l} 7 \\ 0 \end{array})$ (d) $(\begin{array}{l} 5 \\ 3 \end{array})$

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) 31 (b) 99 (c) 70 (d)53

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

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In the following exercises, evaluate.
(a) $(\begin{array}{l} 3 \\ 1 \end{array})$ (b) $(\begin{array}{l} 9 \\ 9 \end{array})$ (c) $(\begin{array}{l} 7 \\ 0 \end{array})$ (d) $(\begin{array}{l} 5 \\ 3 \end{array})$