Question

Given $5$ flags of different colours, how many different signals can be generated if each signal requires the use of $2$ flags, one below the other?

Answer 1

Since, each signal requires the use of $2$ flags.

There will be as many signals as there are ways of filling in $2$ vacant place in succession by the given $5$ flags of different colours.

The upper vacant place can be filled in $5$ different ways by any one of the $5$ flags .

The lower vacant place can be filled in $4$ different ways by any one of the remaining $4$ different flags.

Thus, by multiplication principle, the number of different signals that can be generated is $5\times 4=20$