Question

The number of different signals that can be given using any number of flags using $5$ flags of different colours is :

• A. $325$
• B. $240$
• C. $60$
• D. None of these

Answer 1

The correct option is A $325$

Total number of flags $=5$

Different signals made by one flag only $={}^5{P}_1=5$ ..... $\left(1\right)$

Different signals made by two flags only $={}^5{P}_2=20$ ...... $\left(2\right)$

Different signals made by three flags only $={}^5{P}_3=60$ ..... $\left(3\right)$

Different signals made by four flags only $={}^5{P}_4=120$ ..... $\left(4\right)$

Different signals made by five flags $={}^5{P}_5=120$ ...... $\left(5\right)$

Adding $\left(1\right),\left(2\right),\left(3\right),\left(4\right)$ and $\left(5\right)$, we get

Sum $=5+20+60+120+120=325$

Hence, the number of different signals $=325$