How many different signals can be given using any number of flags from 5 flags of different colours?

Options

A. 720
B. 1440
C. 1956
D. 1950

Explanation

Proceeding as in IIIustration 3, the total number of signals for flags from 6 flags of different colours is `^(6)C_(r)xxr!` But, r can vary from 1 to 6. Therefore, by the fundamental principle of addition
`:.` Required number of signals
`sum_(r=1)^(6)""^(6)C_(r)xxr!""=sum_(r=1)^(6)(6!)/((6-r)!)=1956`