### Permutation and Combination Formula

Permutation is combining several objects from a group by paying attention to the order. In permutations, order matters. Whereas Combination is combining several objects from a group without regard to order. In combinations, order is not taken into account.

Permutation Formula: $$P_r^n=\frac{n!}{(n-r)!}$$
where:

$k!=k.(k-1).(k-2)...1$

$n$ and $r$ is integer. $n \ge r$.

$k!=k.(k-1).(k-2)...1$

$n$ and $r$ is integer. $n \ge r$.

Combination Formula:
$$C_r^n=\frac{n!}{r!.(n-r)!}$$

**Example 1:**$$P_2^4=\frac{4!}{(4-2)!}=\frac{4!}{2!}$$ $4!=4.3.2.1=24$ and $2!=2.1=2$. So, $P_2^4=24/2=12$.

**Example 2:**$$C_3^6=\frac{6!}{3!.(6-3)!}=\frac{6!}{3!.3!}$$ $6!=6.5.4.3.2.1=720$ and $3!=3.2.1=6$. So, $C_3^6=720/36=20$.

Thanks, and happy learning.