Chapter 12: Q20. (page 641)

Evaluate each expression.
$C (12, 4) \cdot C (8, 3)$

Short Answer

Expert verified

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

Step by step solution

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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Evaluate each expression.
$C (12, 4) \cdot C (8, 3)$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Evaluate each expression.C12,4·C8,3

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Evaluate each expression.
$C (12, 4) \cdot C (8, 3)$