Bunuel VeritasPrepKarishma can you help me please?
I am getting confused by these distribution problems. Can you help me differentiate the formulas I must use in each situation?
I had:
- for
x different objects distributed among
n people:
n^x (which i thought was the case here in this question, and still didn't understand why not)
-for
x different rings among
n different fingers: use bars,
number of bars = n-1, total ways =
(x+bars)!/bars!(here, i didn't understand how fingers were treated differently from people, since in both cases they are different among themselves, that is, different fingers but also different people)
-for
x identical objects among
n different things: here as x also repeats, use formula as above but dividing by x!. that is, total ways=
(x+bars)!/x! bars!- for
x identical objects among
n different things, so that each n receives
at least one object:
x-1CbarsHere, for example, 20 fruits among 4 people, so that each receives at least one = 19C3= 19!/16!3!
(here i can't see what the 16! would represent. in the case where people could get 0 fruits, you would divide by the repeated bars (3!) and the repeated fruits (20!), but i can't get what the 16! would be. is it because first you distribute 4 and then all other 16 would be repeated?
Thank you very much in advance. And thank you for all your genius posts, I am learning a lot from you both