Question

Evaluate each expression

$P\left(12,6\right)$

Short answer

The value of $P\left(12,6\right)=665280$.

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $P\left(12,6\right)$.

Step 2. Calculation.

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

Here n=12,r=6

Plugging the values:

$\begin{array}{l}P\left(12,6\right)=\frac{12!}{\left(12-6\right)!}\\ P\left(12,6\right)=\frac{12!}{6!}\\ P\left(12,6\right)=\frac{12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6!}{6!}\\ P\left(12,6\right)=12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\\ P\left(12,6\right)=665280\end{array}$

Step 3. Conclusion.

Hence, the value of $P\left(12,6\right)=665280$.