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.
Solution:
Given:5 Flags
Way of generating signal using 2 different flags $={ }^{5} \mathrm{P}_{2}$ (way of selecting 2 things out of 5 things with considering arrangement.)
Way of generating signal using 3 different flags $={ }^{5} \mathrm{P}_{3}$
Way of generating signal using 4 different flags $={ }^{5} \mathrm{P}_{4}$
Way of generating signal using 5 different flags $={ }^{5} P_{5}$
So total number of ways $={ }^{5} P_{2}+{ }^{5} P_{3}+{ }^{5} P_{4}+{ }^{5} P_{5}$
$=20+60+120+120$
$=320$