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Q20.

Expert-verified

Algebra 2

Found in: Page 641

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Evaluate each expression.

$C (12, 4) \cdot C (8, 3)$

The value of $C (12, 4) \cdot C (8, 3) = 27720$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given to evaluate the expression $C (12, 4) \cdot C (8, 3)$ .

Step 2. Calculation.

When n objects are available and r are to be picked then the number of combinations is given by $C (n, r) = \frac{n!}{(n - r)! r!}$

Using the formula:

$\begin{array}{l} C (12, 4) \cdot C (8, 3) = \frac{12!}{(12 - 4)! 4!} \cdot \frac{8!}{(8 - 3)! 3!} \\ C (12, 4) \cdot C (8, 3) = \frac{12!}{8! 4!} \cdot \frac{8!}{5! 3!} \\ C (12, 4) \cdot C (8, 3) = \frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5!}{8! \cdot 4 \cdot 3 \cdot 2 \cdot 1} \cdot \frac{8!}{5! \cdot 3 \cdot 2 \cdot 1} \\ C (12, 4) \cdot C (8, 3) = 27720 \end{array}$

Step 3. Conclusion.

Hence, the value of $C (12, 4) \cdot C (8, 3) = 27720$ .

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