Friday, September 7, 2007
Problem 5
"In a shop, there are k kinds of postcards. We want to send postcards to n friends. How many different ways this can be done? What happens if we want to send them different cards? What happends if we want to send two different cards to each of them (but different persons may get the same card) ?"
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3 comments:
"In a shop, there are k kinds of postcards. We want to send postcards to n friends. How many different ways this can be done?"
-> k^n.
"What happens if we want to send them different cards?"
-> C(k,n) (k chooses n).
"What happens if we want to send two different cards to each of them (but different persons may get the same card)?"
-> for each person, we choose 2 cards (k chooses 2), and then repeat for n person. Thus, the answer is (C(k,2))^n.
Opps! I guess my second answer was wrong. It should be n!C(k,n) = k(k-1)(k-2)...(k-n+1).
Thanks Loc. I have the same solution with you :)
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