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