# Counting!

• Jun 18th 2008, 05:32 AM
santatrue
Counting!
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?
• Jun 18th 2008, 07:11 AM
Soroban
Hello, santatrue!

Quote:

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 had to list the possiblities . . . *blush*

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: .$\displaystyle 4 + 12+6+12+1 \:=\:\boxed{35\text{ ways}}$

• Jun 18th 2008, 07:11 AM
Plato
Quote:

Originally Posted by santatrue
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?

Go on, put one scarf into each box.
Now how many ways can we put the four identical scarves left into the four different boxes?