Question

Question on Permutation:

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

The answer provided was '' The order of the flags determines the meaning of the signal so in this case we calculate the number of permutations of 2 to 5 .

So what is the numerical answer for this question? I do not understand because is this question supposed to be repetition of flags allowed or no repetition?

Answer 1

The provided answer is saying that given five flags \(f_1,\ldots,f_5\), that a permutation of \(f_1f_2\) is different from \(f_2f_1\) and so these should be counted individually.

This means the total number of different arrangements you can make is \({}_5\mathrm P_2=\dfrac{5!}{(5-2)!}=\dfrac{5!}{3!}=5\times4=20\). You have five different choices for the first flag, leaving you with four different choices for the second. This is assuming repetition is not allowed, which seems reasonable given that you're only told there are five different flags, and there's nothing explicitly said about there being more than one copy of any given flag. If repetitions were possible, you would have \(5\times5=25\) possible arrangements.