Question

The number of signals that can be given using any number of flags of 5 different colors, is

• A. $225$
• B. $325$
• C. $215$
• D. $315$

Answer 1

Answer: (B)

$325$

Total number of signals can be made by using at a time one or more but not larger than five flags.
Now number of signals when r flags are used at a time from 5 flags is equal to the number of arrangement of 5 taking r at a time i.e ${}^5{P}_r(r=1,2,...5)$
$\therefore$ Required ways
${}^5{P}_1{+}^5{P}_2+....{+}^5{P}_5$
$=5+20+60+120+120$
$=325$