I have 7 different signal cards that I can flash 5 at a time. How many different signals can I make?
Assuming order is important:
The first card can be any of the 7,
the second any of the remaining 6
the third any of the remaining 5,
etc
So the total number is $\displaystyle 7 \times 6 \times 5 \times 4 \times 3=\frac{7!}{2!}=
\left( {\begin{array}{*{20}c}
7 \\
5 \\
\end{array}} \right)5!
$
RonL