Question

Total number of different signals that can be made using atleast $3$ flags from $5$ flags of different colours is

Answer 1

The signals can be made using $3$ or more flags at a time.
$\therefore$the total number of signals is equal to
${}^5{P}_3+{}^5{P}_4+{}^5{P}_5$
$=\frac{5!}{2!}+\frac{5!}{1!}+\frac{5!}{0!}$
$=(5\times 4\times 3)+(5\times 4\times 3\times 2)+(5\times 4\times 3\times 2\times 1)=60+120+120$
$=300$