Combinatorics problem

  • Thread starter swtlilsoni
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  • #1
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Homework Statement



You have 3 types of postcards. There are 5 of each type. How many ways can you send the 15 postcards to 15 friends, if each friend receives 1.


The Attempt at a Solution



I thought it would merely be 15!/(3*5!)
 

Answers and Replies

  • #2
CompuChip
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Are you sure about the 3 * 5! ?
 
  • #3
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Are you sure about the 3 * 5! ?
because there are three sets of five identicals
 
  • #4
tiny-tim
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hi swtlilsoni! :smile:
because there are three sets of five identicals


if there were 10 friends, and 2 sets of five identicals, would you use 10!/2*5! ? :wink:
 
  • #5
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Ohh okay so it would be 5!3!
 
  • #6
CompuChip
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Can you explain that to us, or are you just guessing now? :)
 
  • #7
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it's because it has to be multiplied. For every rearrangement of five identicals, there are two more rearrangements of the others
 
  • #8
tiny-tim
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hi swtlilsoni! :smile:

(just got up :zzz: …)
it's because it has to be multiplied. For every rearrangement of five identicals, there are two more rearrangements of the others

the general rule for selecting a of one type, b of another, … z of another, from n altogether (with a+b+… +z = n), is:

n!/a!b!…z!​

for only two types, that reduces to the familiar:

n!/a!b! = n!/a!(n-a)! = nCa :wink:
 

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