- #1

- 465

- 4

## Homework Statement

I have:

4 Blue pens

16 Green pens

7 Red pens

11 Yellow pens

If I lay out all the pens in a single row, how many different arrangements does this system have?

## Homework Equations

$$_nC_r = \frac{n!}{r!(n-r)!}$$

## The Attempt at a Solution

*Procedure:*

Basically the number of ways I can arrange the 4 blue pens within the 38 spaces, and then the number of ways I can arrange the 16 green pens within the 38-4 spaces, etc.

$$n = Total pens = 38$$

Total Number of Arrangements $$ = \sum(_{(n - \sum r_i)}C_{(r_i)}) $$

$$_{(38)}C_4 + _{(38-4)}C_{16} + _{(38-4-16)}C_7 +_{(38-4-16-7)}C_{11}$$

But doing it this way depends on the order in which I calculate the combinations. Clearly doing something wrong.