- #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!)

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- Thread starter swtlilsoni
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- #1

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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.

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

- #2

CompuChip

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Are you sure about the 3 * 5! ?

- #3

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because there are three sets of five identicalsAre you sure about the 3 * 5! ?

- #4

tiny-tim

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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! ?

- #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? :)

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- #8

tiny-tim

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(just got up :zzz: …)

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

n!/a!b! = n!/a!(n-a)! = ^{n}C_{a}

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