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 #4
avatar+11054 
+1
2 hours ago
 #13
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I can explain more but I want to stress that I am not sure if this is completely correct. 

My answer is the same as CPhill got with his formula but I am still not convinced that my method is right.

It is the things you are questioning that i am not sure about  but here is your explanation.

 

(b) I also bought 7 different postcards. How many ways can I send the postcards to my 3 friends, so that each friend gets at least one postcard?

 

The original answer was 15, that was if all the cards were the same.

 

possible numbers of bags each (total 7)   

511     3  ways if all the same   7*6=42              3*42=126

the first person can get any of the 7 postcards, the second person gets any of the 6 remaining, the 3rd person gets the rest.

Hence 7*6* the number of ways if the cards had been all the same.

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421     6  ways if all the same   7*6C2=105       6*105=630

the first person can get any of the 7 postcards, the second person gets any 2 of the 6 remaining, the 3rd person gets the rest.

Hence 7*6C2 times the number of ways if the cards had been all the same.

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331     3  ways if all the same   7*6C3=140       3*140=420

The first person can get any of the 7 postcards, the second person gets any 3 of the 6 remaining, the 3rd person gets the rest.

Hence 7*6C3 times the number of ways if the cards had been all the same.

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322     3 ways if all the same   7C2*5C2=210     3*210=630

The first person can get any 2 of the 7 postcards, the second person gets any 2 of the 5 remaining, the 3rd person gets the rest.

Hence 7C2*5C2 = 210 times the number of ways if the cards had been all the same.

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Total   15 ways if all the same 1806 ways if all are different

6 hours ago

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