Question

How many different signals can be given by using any number of flags from six flags of different colors?

Answer 1

By alteration in the arrangement of flags, the signals will change. So we have to find permutations i.e. arrangements of flags. We are at liberty to use any number of flags at a time. Therefore the required number of signals is
${}^6{P}_1$ + ${}^6{P}_2$ + ${}^6{P}_3$ + ${}^6{P}_4$ + ${}^6{P}_5$ + ${}^6{P}_6$
= 6 + 30 + 120 + 360 + 720 + 720 = 1956.