Question

How many different signals can be made by $5$ flags from $8$ flags of different colours?

Answer 1

The total number of signals is the number of arrangements of $8$ flags by taking $5$ flags at a time.

Hence, required number of signals${=}^8{P}_5=\frac{8!}{(8-5)!}=\frac{8!}{3!}=\frac{8\times 7\times 6\times 5\times 4\times 3!}{3!}=6720$