How many ways can eight identical svarves be placed into four disingusihable boxes( boxes you can tell apart), if each box must contain at least one scarf?
Hello, santatrue!
I had to list the possiblities . . . *blush*How many ways can eight identical scarves be placed into four distinguishable boxes
( boxes you can tell apart), if each box must contain at least one scarf?
I found five scenarios.
$\displaystyle 5,1,1,1$ . . . and there are $\displaystyle 4$ ways.
$\displaystyle 4,2,1,1$ . . . and there are $\displaystyle \frac{4!}{2!} = 12$ ways.
$\displaystyle 3,3,1,1$ . . . and there are $\displaystyle \frac{4!}{2!2!} = 6$ ways.
$\displaystyle 3,2,2,1$ . . . and there are $\displaystyle \frac{4!}{2!} = 12 $ ways.
$\displaystyle 2,2,2,2$ . . . and there is $\displaystyle 1$ way.
Therefore, there are: .$\displaystyle 4 + 12+6+12+1 \:=\:\boxed{35\text{ ways}}$