Find the number of different signals that can be generated by arranging at least 22 flags in order(one below the other) on a vertical staff, if 55 different flags are available.


Answer:

320320

Step by Step Explanation:
  1. A signal can consist of either 22 flags, 33 flags, 44 flags or 55 flags. Now, let us count the possible number of signals consisting of 22 flags, 33 flags, 44 flags, and 55 flags separately and then add the respective numbers.
  2. There will be as many 22 flag signals as there are ways of filling in 22 vacant places in succession by the 55 flags available.
    By the fundamental principle of counting, the number of ways is 5×4=205×4=20
  3. Similarly, the number of 3 flag signals is 5×4×3=605×4×3=60, the number of 44 flags signals is 120120 and the number of 55 flags signals is 120120.
  4. Therefore, the required no. of signals =20+60+120+120=20+60+120+120=320.=320.

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