Question

Given 3 flags of different colours, how many different signals can be generated, if a signal requires the use of 2 flags one below the other?

Answer 1

There will be as many signals as there are ways of filling in $2$ vacant places in succession by the $3$ flags of different colours. The upper vacant place can be filled in $3$ different ways by anyone of the 3 flags; following which, the lower vacant place can be filled in $2$ different ways by anyone of the remaining $2$ different flags. Hence, the required number of signals
$=3\times 2=6.$