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

Explanation

A signal can consist of either 2 flags, 3 flags, 4 flags, or 5 flags. Now , let us count the possible number of signals conisting of 2 flags, 3 flags, 4 flags, and 5 flags separately and then add the respective numbers.

There will be as many 2 flag signals are there are ways filling in 2 vacant places in succession by the flags available. By the multiplication rule, the number of ways is `5xx4=20`.
Similarly, there will be as many 3 flag signals as there are ways of filling in 3 vacant places in succession by the 5 flags.

The number of ways is `5xx4xx3=60`. Continuing the same way, we find that the number of 4 flag signals `=5xx4xx3xx2xx1=120` and the number of 5 flag signals`=5xx4xx3xx2xx1=120`.
Therefore, the required no. of signals `=20+60+120+120=320`.