Explanation

(d)
Given number of flags$= 5$
Number of signals formed using one flag$= {\ ^{5}P}_{1} = 5$
Similarly, using 2 flags$= {\ ^{5}P}_{2}$
Using 3 flags$= {\ ^{5}P}_{3}$
Using 4 flags$= {\ ^{5}P}_{4}$
Using 5 flags$= {\ ^{5}P}_{5}$
$\therefore$ Total number of signals that can be formed
$= {\ ^{5}P}_{1} + {\ ^{5}P}_{2} + {\ ^{5}P}_{3} + {\ ^{5}P}_{4} + {\ ^{5}P}_{5}$
$= 5 + 20 + 60 + 120 + 120$
$= 325$