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 ^@5^@ different flags are available.


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Answer:

^@320^@

Step by Step Explanation:
  1. 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.
  2. 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^@
  3. 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^@.
  4. Therefore, the required no. of signals ^@ = 20 + 60 + 120 + 120^@^@ = 320.^@

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