Question

The number of signals that can be generated by using $6$ differently coloured flags, when any number of them may be hoisted at a time, is

• A. $1956$
• B. $1957$
• C. $1958$
• D. $1959$

Answer 1

The correct option is A $1956$

Using $1$ flag ${}^6{P}_1$ signals can be generated

Using $2$ flag ${}^6{P}_2$ signals can be generated

Using $3$ flag ${}^6{P}_3$ signals can be generated

Using $4$ flag ${}^6{P}_4$ signals can be generated

Using $5$ flag ${}^6{P}_5$ signals can be generated

Using $6$ flag ${}^6{P}_6$ signals can be generated

So total

${}^6{P}_1{+}^6{P}_2{+}^6{P}_3{+}^6{P}_4{+}^6{P}_5{+}^6{P}_{6}6+30+120+360+720+720=1956$