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From a collection of 5 different colors of flags(at least 5 flags of each color) how many different signals can be made by displaying them in a vertical line, using any number of flags from 1 to 5?

I tried to answer like this:

$$N= (P_5^5)(P_5^5)$$

$$N= (120)(120)$$

$$N= 14 400$$

I don't know if it's correct.

prog_SAHIL
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Madisson
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2 Answers2

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At each of the points, you have six choices: a flag of one of the $5$ colors, or none.

But there needs to be at least one flag, hence $6^5 -1$ different signals.

true blue anil
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You have 5 spaces to fill (Because you can use upto 5 flags)

There are total 6 ways to fill each spot (5 different colored flags or leave it empty)

This will give us $$6*6*6*6*6 = 6^5$$

Now we will leave the case where all the spots are empty,

So, $$6^5-1$$

prog_SAHIL
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  • Its equal to 325 – Madisson Jan 01 '18 at 12:29
  • @Madisson I misread the question. I thought you just had 1 flag of each color. Check the edited answer. – prog_SAHIL Jan 01 '18 at 12:30
  • Yes. I notice that. Thank you for helping.The colors only matters in this problem right? I have a question. jow come you can leave an empty position? – Madisson Jan 01 '18 at 12:33
  • @Madisson Empty positions helps us to change the number of flags from 1 to 5. If we leave 1 empty position we have a signal with 4 flags. If we leave 2 empty positions we have a signal with 3 flags and so on upto 4 empty spaces i,e. 1 flag signal. – prog_SAHIL Jan 01 '18 at 12:39
  • Can i ask another question? If i wanty question to look like this.You edited it right? What should i do if i only u sed mobile phone? – Madisson Jan 01 '18 at 12:48
  • By the way.Repetition is allowed here right? – Madisson Jan 01 '18 at 12:49
  • @Madisson Yes repetition is allowed else we would have to check evaluate each case differently (1 flag,2 flag,..so on). – prog_SAHIL Jan 01 '18 at 13:18
  • To use MathJax editing enloce your expressions between $ (dollar signs.) – prog_SAHIL Jan 01 '18 at 13:19
  • @Madisson Comments are not meant for extended discussion. You should move this conversation to chatbox if you would like to continue. – prog_SAHIL Jan 01 '18 at 13:21