The Chemistry departmental office has 800 black dry-erase markers. The 25 members of the department may take as many as they like. If 46 markers are taken the ﬁrst day, how many different distributions to the faculty members are possible?

Question

anonymous · Answer

@mukushla  @eliassaab

anonymous · Answer

@siddhantsharan  @hartnn

anonymous · Answer

Umm.
Total markers chosen = 46
Let total markers chosen by person 1 = x1  -- (1 is in the subscript)
by person 2 = x2
person 3 = x3.....
.
,
person 25 = x25

Therefore 
x1 + x2 + x3 ........... + x25 = 46
Now, Find the non negative integral solutions for this using the formula.

anonymous · Answer

So it will be
$$\left(\begin{matrix}46+25-1 \ 25-1\end{matrix}\right)$$

anonymous · Answer

$$\left(\begin{matrix}70 \ 24\end{matrix}\right)$$

anonymous · Answer

Can...we Do.this by..Permutation and combination.....Since..i have nt studied those..things which u posted nw

anonymous · Answer

LEmme try.

anonymous · Answer

ok...

anonymous · Answer

Okay I can figure out 2 more ways to do this.
First. 
Lets take a parallel problem to simplify matters.

anonymous · Answer

Let there be 3 members in the department and say 5 markers.
Now these are 5 similar objects to be divided into three people. 
So lets consider two dividers. 
Basically, wherever we place this "divider" the objects are divided accordingly. 
For example:
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