SOLUTION: How many different signals can be made by using at at most 2 distinct(ordered) flags if there are five flags to choose from ?

Question 1176487: How many different signals can be made by using at at most 2 distinct(ordered) flags if there are five flags to choose from ?
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
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At most 2 flags means 2 or 1 or 0 (if consider the absence of flags as a special signal).

So, you can display 5 signals, showing any one single separate flag of five flags that you have.


Next, you can display 5*4 = 20 signals, showing ordered pairs of distinct flags.


So, you can display, in total, 5 + 20 = 25 signals using 1 or 2 flags.


If there is an agreement that the absence of flags is a special signal, too, then you can display 25 + 1 = 26 signals.

Solved, answered and explained.

Notice that 26 is exactly the number of letters in English alphabet (!)

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