Question

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

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

Answer 1

Answer: (C)

$64$

Signals of $1$ flag $={}^4{C}_1=4$
$2$ flags$={}^4{C}_{2}2!=12$
$3$ flags$={}^4{C}_{3}3!=24$
$4$ flags$={}^4{C}_{4}4!=24$
Therefore, total $=64$.