Sangsuddha
Level
pending
In how many ways can 5 letters be mailed if 4 mailboxes are available? (there can be empty mailboxes)
56
05
72
20
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1 solution
All of these can be solved by direct application of Stars and Bars.
The formula for Stars and Bars is given by: {n+r-1\ choose n}where n is the number of "objects" and r is the number of "groups we are trying to find the number of ways to distribute 5 letters to 4 mailboxes. The "objects" here are the letters,and they are to be distributed into "groups," which are the mailboxes. So the number of ways are {5+4-1 \ choose 5} = {8 \ choose 5}=56