Chapter 11: Q. 308 (page 1069)

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

Short Answer

Expert verified

The value is $7, 1, 1, 126$ respectively

Step by step solution

Part (a) Step 1: Given information

Given the binomial coefficient $(\begin{array}{l} 7 \\ 1 \end{array})$

Part (a) Step 2:Calculate using the formula

Calculating, we get

$(\begin{array}{l} 7 \\ 1 \end{array}) = \frac{n!}{r! (n - r)!} (\begin{array}{l} 7 \\ 1 \end{array}) = \frac{7!}{1! (7 - 1)!} (\begin{array}{l} 7 \\ 1 \end{array}) = \frac{7!}{1! \times 6!} (\begin{array}{l} 7 \\ 1 \end{array}) = \frac{7 \times 6!}{1 \times 6!} (\begin{array}{l} 7 \\ 1 \end{array}) = 6$

Part (b): Step 1: Given information

Given binomial coefficient $(\begin{array}{l} 5 \\ 5 \end{array})$

Part (b) Step 2: Calculate using the formula

Calculating, we get

$(\begin{array}{l} n \\ n \end{array}) = 1 (\begin{array}{l} 5 \\ 5 \end{array}) = 1$

Part (c) Step 1: Given information

Given binomial coefficient $(\begin{array}{l} 9 \\ 0 \end{array})$

Part (c) Step 2: Calculating using the formula

Calculating, we get

$(\begin{array}{l} n \\ 0 \end{array}) = 1 (\begin{array}{l} 9 \\ 0 \end{array}) = 1$

Part (d) Step 1: Given information

Given binomial coefficient $(\begin{array}{l} 9 \\ 5 \end{array})$

Part (d) Step 2: Calculating using the formula

Calculating, we get

$(\begin{array}{l} 9 \\ 5 \end{array}) = \frac{9!}{5! (9 - 5)!} (\begin{array}{l} 9 \\ 5 \end{array}) = \frac{9!}{5! \times 4!} (\begin{array}{l} 9 \\ 5 \end{array}) = \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4!}{5! \times 4!} (\begin{array}{l} 9 \\ 5 \end{array}) = 126$

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

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2:Calculate using the formula

Part (b): Step 1: Given information

Part (b) Step 2: Calculate using the formula

Part (c) Step 1: Given information

Part (c) Step 2: Calculating using the formula

Part (d) Step 1: Given information

Part (d) Step 2: Calculating using the formula

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In the following exercises, evaluate.a.71b.55c.90d.95

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2:Calculate using the formula

Part (b): Step 1: Given information

Part (b) Step 2: Calculate using the formula

Part (c) Step 1: Given information

Part (c) Step 2: Calculating using the formula

Part (d) Step 1: Given information

Part (d) Step 2: Calculating using the formula

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