Question

The number of different signals can be given by using any number of flags from $4$ flags of different colours is

• A. $24$
• B. $256$
• C. $64$
• D. $60$

Answer 1

The correct option is C $64$

$\because$ The order of the flags also makes a new signal.

$\therefore$ Number of signals made by using only one flag a time $=4$
Number of signals made by using $2$ flags a time
$=4\times 3=12$
Number of signals made by using $3$ flags a time
$=4\times 3\times 2=24$
Number of signals made by using all flags a time
$=4\times 3\times 2\times 1=24$

Hence, total possible number of signals are
$24+24+12+4=64$