Question

The number of signals that can be formed using 6 flags of different colours taking $1$ or more flags at a time is ?

• A. $1956$
• B. $1256$
• C. $1164$
• D. $1260$

Answer 1

The correct option is A $1956$

Number of signals with one flag $=6$

Number of signals with $2$ flags ${=}^6{P}_2=30$

Number of signals with $3$ flags ${=}^6{P}_3=120$

Number of signals with $4$ flags ${=}^6{P}_4=360$

Number of signals with $5$ flags ${=}^6{P}_5=6!=720$

Number of signals with $6$ flags ${=}^6{P}_6=720$

Total number of signals $=720+720+360+120+30+6=1956$