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Help!

How many permutations of $3$ letters out of the word BANANA can be made?

The full letter BANANA will only give you $60$ different ways: ${ 6 ! } / ( 1 ! 3 ! 2 ! ) = 720 / 12 = 60 $

But since they only want $3$ letters, the probability should be double

Is the answer $6P_3 = 120$ or $(6!/3!\times2!)/2 = 120$?

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    What have you tried? This is a relatively easy question, surely you must have tried something yourself (or if you haven't then please do so now, since this is not a 'do my homework for free' service). – 2017-01-18
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    I did but I'm not good in maths. I tried 6P3 = 120 or (6!/3!*2!)/2 = 120 – 2017-01-18
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    Show what you did, and we will be more motivated to help you with it. – 2017-01-18
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    @ski, use this tool http://www.careerbless.com/calculators/word/index.php type the word 'BANANA' and see question number 16. this is useful if you want to try with various examples. – 2017-01-18
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    @Kiran thanks! It's very helpful – 2017-01-18

1 Answers 1

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Add up the following:

  • Number of permutations of AAA: $\frac{3!}{3!}=1$
  • Number of permutations of AAB: $\frac{3!}{2!1!}=3$
  • Number of permutations of AAN: $\frac{3!}{2!1!}=3$
  • Number of permutations of ABN: $\frac{3!}{1!1!1!}=6$
  • Number of permutations of ANN: $\frac{3!}{1!2!}=3$
  • Number of permutations of BNN: $\frac{3!}{1!2!}=3$
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    That's what we did in class earlier (Click the word "Photo" in the blue color). But we were confused about whether to add or multiply. So we thought it was wrong (as you can see with the word "wrong" on the board) – 2017-01-18
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    If added together, the answer will be 19? – 2017-01-18
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    @JuxeskiScolowski: As the answer says - you should add. And yes, $1+3+3+6+3+3=19$. – 2017-01-18
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    Thanks alot! (Sorry we're not good in maths!) – 2017-01-18
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    @JuxeskiScolowski: You're welcome :) – 2017-01-18