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How many different signals can be made by using exactly 3 different flags if there are 5 different flags from which to select?

Mar 7th, 2015

Here, we're looking for the number of possible permutations of 3 flags Why is this?

Well, a permutation is an ordered combination. If we have flags ABCDE, then signal ABC is different to signal BAC, for example.

So how many permutations are there? There's a fairly simple formula. If you have n possible objects, and you have to combine r of them, then there are:

n!/(n-r)! possible permutations.

The ! is the symbol for 'factorial', and it means multiply n by n-1, and n-2, and.... so on down to 1.

In this example we have n = 5 and r = 3. So n! = 5! = 5x4x3x2x1, and (n-r)! = (5-3)! = 2! = 2x1. So the number of possible signals is:

5x4x3x2x1 / 2x1 

= 5x4x3

= 60


Hope this helped!

Mar 7th, 2015

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