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

Hint:Total number of flags are 5. Signals generated by at least 2 flags means signals generated when 2, 3, 4 and 5 flags are used. Thus find all the cases and add them to get the number of different signals.

Complete step-by-step answer:
We have been told that there are 5 different flags. Thus, the total number of flags = 5.
Now, we have been told to find the number of different signals that can be generated by arranging at least 2 flags in order.
We have been told the word “at least” which means that the signals can be arranged with 2, 3, 4 or 5 flags. Hence, we need to find all the cases. Here no repetition of flags can be done.
First let us find the number of signals generated by using 2 flags.
We need to draw the flag, one below the other in order.

5

4

$\therefore$ The number of signals generated using 2 flags $=5\times 4 = 20….. (1)$.
Now let us find the number of signals generated by using 3 flags.

5

4
3

$\therefore$ Number of signals $=5\times 4\times 3 = 60……. (2)$.
Number of signals that are generated by using 4 flags can be found using,

5

4
3
2

Number of signals $=5\times 4\times 3\times 2 = 120……..(3)$
Now let us find the number of signals that can be generated by using 5 flags.

5

4
3
2
1

$\therefore$ Number of signals = $=5\times 4\times 3\times 2\times 1 = 120……..(4)$
Now let us add all the cases (1), (2), (3) and (4).
Total number of signals generated = 20 + 60 + 120 + 120 = 320
Total number of different signals generated are 320 signals.
Note: As there is no repetition of flag, thus you can choose any 1 of the flag from 5 flags. For choosing the ${{2}^{nd}}$ flag there are 4 options, remaining after choosing ${{1}^{st}}$ flag. Similarly, for choosing ${{3}^{rd}}$ flag there are 3 options left and thus it goes on.