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Chapter 12: Q5. (page 641)

Evaluate each expression
$P (6, 3)$

Short Answer

Expert verified

The value of $P (6, 3) = 120$ .

Step by step solution

01

Step 1. Given Information.

Given to evaluate the expression $P (6, 3)$ .

02

Step 2. Calculation.

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

Here n=6,r=3

Plugging the values:

$\begin{array}{l} P (6, 3) = \frac{6!}{(6 鈭� 3)!} \\ P (6, 3) = \frac{6!}{3!} \\ P (6, 3) = \frac{6 鈰� 5 鈰� 4 鈰� 3!}{3!} \\ P (6, 3) = 6 鈰� 5 鈰� 4 鈰� \\ P (6, 3) = 120 \end{array}$

03

Step 3. Conclusion.

Hence, the value of $P (6, 3) = 120$

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