Chapter 12: Q21. (page 641)

Evaluate each expression
$C (9, 3) \cdot C (6, 2)$

Short Answer

Expert verified

The value of $C (9, 3) \cdot C (6, 2) = 1260$ .

Step by step solution

Step 1. Given Information.

Given to evaluate the expression $C (9, 3) \cdot C (6, 2)$ .

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:

$\begin{array}{l} C (9, 3) \cdot C (6, 2) = \frac{9!}{(9 - 3)! 3!} \cdot \frac{6!}{(6 - 2)! 2!} \\ C (9, 3) \cdot C (6, 2) = \frac{9!}{6! 3!} \cdot \frac{6!}{4! 2!} \\ C (9, 3) \cdot C (6, 2) = \frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!}{6! \cdot 3 \cdot 2 \cdot 1} \cdot \frac{6!}{4! \cdot 2 \cdot 1} \\ C (9, 3) \cdot C (6, 2) = 1260 \end{array}$

Step 3. Conclusion.

Hence, the value of $C (9, 3) \cdot C (6, 2) = 1260$ .

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Evaluate each expression
$C (9, 3) \cdot C (6, 2)$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Evaluate each expressionC9,3·C6,2

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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Pure Maths

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Study anywhere. Anytime. Across all devices.

Evaluate each expression
$C (9, 3) \cdot C (6, 2)$