Question

Find the number of signal that can be used by 6 flags of different colours taking one or more at a time.

Answer 1

Let $W$ denote the number of ways.
$W{=}^6{P}_1{+}^6{P}_2{+}^6{P}_3{+}^6{P}_4{+}^6{P}_5{+}^6{P}_6$
Using ${}^n{P}_r=\frac{n!}{(n-r)!}$
$W=6+30+120+360+720+720=1956$