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Chapter 12: Q6. (page 641)

Evaluate each expression
$C (4, 2)$

Short Answer

Expert verified

The value of $C (4, 2) = 6$ .

Step by step solution

01

Step 1. Given Information.

Given to evaluate the expression $C (4, 2)$ .

02

Step 2. Calculation.

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

Here n=4,r=2

Plugging the values:

$\begin{array}{l} C (4, 2) = \frac{4!}{(4 - 2)! 2!} \\ C (4, 2) = \frac{4!}{2! 2!} \\ C (4, 2) = \frac{4 \cdot 3 \cdot 2!}{2 \cdot 1 \cdot 2!} \\ C (4, 2) = \frac{12}{2} \\ C (4, 2) = 6 \end{array}$

03

Step 3. Conclusion.

Hence, The value of $C (4, 2) = 6$ .

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