How many different signals can be given using any number of flags from 4 flags of different colours?

Explanation

The signals can be made by using one or more flags at a time. Hence, by the fundamental principal of addition, the total number of signals
`=.^(4)P_(1)+.^(4)P_(2)+.^(4)P_(3)+.^(4)P_(4)`
`=4+(4xx3)+(4xx3xx2)+(4xx3xx2xx1)`
`=4+12+24+24=64`