Hello, jfz23!

I believe this is a trick question . . .There are nineitemsindistinguishable

and they are to be divided evenly among three assembly lines.

(A) How many ways can this be done?

The key word is "indistinguishable".

The nine items areidentical: .

I see onlyone wayto distribute the items:

. .

Another trick question . . .(B) Two of the items are used and seven are new.

What is the probability that agets both used items?particularline

If they had said "both used items are in the same line" (any of the lines),

. . we would use a certain approach.

Since they said "a particular line", the approach is different.

For simplicity, assume that the nine items are distinguishable.

They would be: . . where and are used.

There are: . possible arrangements.

Suppose the particular line is Line 1.

There is 1 way for A and B to be in Line 1.

Then there are: . ways to distribute the other seven items.

Hence, there are: . ways for and to be in Line 1.

Therefore: .