# How do you figure out the number of combinations in 4 digit numbers?

Apr 13, 2018

$24 \text{ combinations}$

#### Explanation:

$\text{the possible combinations are}$

$\text{using the 4 digits 1234}$

$\left(\begin{matrix}1 & 2 & 3 & 4 \\ 1 & 2 & 4 & 3 \\ 1 & 3 & 2 & 4 \\ 1 & 3 & 2 & 4 \\ 1 & 3 & 4 & 2 \\ 1 & 4 & 2 & 3 \\ 1 & 4 & 3 & 2\end{matrix}\right) = 6 \left(\begin{matrix}2 & 1 & 3 & 4 \\ 2 & 1 & 4 & 3 \\ 2 & 3 & 1 & 4 \\ 2 & 3 & 4 & 1 \\ 2 & 4 & 1 & 3 \\ 2 & 4 & 3 & 1\end{matrix}\right) = 6$

$\left(\begin{matrix}3 & 1 & 2 & 4 \\ 3 & 1 & 4 & 2 \\ 3 & 2 & 1 & 4 \\ 3 & 2 & 4 & 1 \\ 3 & 4 & 1 & 2 \\ 3 & 4 & 2 & 1\end{matrix}\right) = 6 \left(\begin{matrix}4 & 1 & 2 & 3 \\ 4 & 1 & 3 & 2 \\ 4 & 2 & 1 & 3 \\ 4 & 2 & 3 & 1 \\ 4 & 3 & 1 & 2 \\ 4 & 3 & 2 & 1\end{matrix}\right) = 6$

$\Rightarrow \text{ number of combinations } = 24$

$\text{this may be calculated using the "color(blue)"factorial}$

•color(white)(x)n! =n(n-1)(n-2) ...... xx3xx2xx1

"number of combinations "=4! =4xx3xx2xx1=24