Question

Find the number of different signals that can be generated by arranging at least $2$ flags in order (one below the other) on a vertical staff, if five different flags are available?

Answer 1

Step $1:$
Finding number of signals for $2$ flags.
Number of ways for first flag $=5$
Number of ways for second flag $=4$
$\therefore$ Required number of signals $=5\times 4=20$

Step 2:
Finding number of signals for $3$ flags.
Number of ways for first flag $=5$
Number of ways for second flah $=4$
Number of ways for third flag $=3$
$\therefore$ Required number of signals $=5\times 4\times 3=60$

Step 3:
Finding number of signals for $4$ flags.
Number of ways for first flag $=5$
Number of ways for second flag $=4$
Number of ways for third flag $=3$
Number of ways for fourth flag $=2$
$\therefore$ Required number of signals $=5\times 4\times 3\times 2=120$

Step $4:$
Finding number of signals for $5$ flags.
Number of ways for first flag $=5$
Number of ways for second flag $=4$
Number of ways for third flag $=3$
Number of ways for fourth flag $=2$
Number of ways for fourth flag $=1$
$\therefore$ Required number of signals $=5\times 4\times 3\times 2\times 1=120$

Step $5:$
$\therefore$ Total number of signals $=20+60+120+120=320$