Find the number of different signals that can be generated by ar | Math Question and Answer

Answer:

$320$

Step by Step 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 consisting 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 as there are ways of filling in $2$ vacant places in succession by the $5$ flags available.
By the fundamental principle of counting, the number of ways is $5 \times 4 = 20$
Similarly, the number of 3 flag signals is $5 \times 4 \times 3 = 60$ , the number of $4$ flags signals is $120$ and the number of $5$ flags signals is $120$ .
Therefore, the required no. of signals $= 20 + 60 + 120 + 120$ $= 320.$

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