Question

Given $5$ flags of different colors, how many different signals can be generated, if the use of $2$ flags one below the other are required to generate the signal?

• A. $20$
• B. $30$
• C. $24$
• D. $36$

Answer 1

The correct option is A $20$

It is given that signal is generated by using $2$ flags of different colors one below the other.
For example: Given below figure shows how signals are generated from two flags.

So, total number of signals is equal to number of ways of filling $2$ vacant places in succession by $5$ flags of different colors.

The upper vacant place can be filled in $5$ different ways.
And, the lower one in $4$ different ways by any one of the remaining $4$ flags.

Hence, by fundamental principle of counting, the required number of signals are $5\times 4=20$