Distributing two bosons among four states

[Mechdude]

Homework Statement

calculate the possible number of ways of distributing 2 particles among four energy startes when:
particle are distinguishable and there is no restriction on the occupancy of the energy state

Homework Equations

$$\frac{(n+g-1)}{n!(g-1)!}$$

The Attempt at a Solution

using the formula i get 10 ,
but on enumerating manually i get 16
since there will be four ways the two particles can go into the four states two at a time ,
then six ways they can go into t the four state one at a time , but since thy can be distinguished there's another six when they are interchanged ,
( 2 _ _ _ )
( _ 2 _ _ )
( _ _ 2 _ )
( _ _ _ 2 )

( a1 a2 __ __ )
(a1 __ a2 __ )
(a1 __ __ a2 )
(__ a1 a2 __ )
(__ a1 __ a2 )
(__ __ a1 a1)

these last six can be interchanged as i said tho get a total of 16.

i'm required to calculate this, but I am getting different results using the different methods what's up?

 

[Matterwave]

Bosons are indistinguishable, and so I think probably your equation there is for indistinguishable bosons.

 

[Mechdude]

my bad,
formula should have been
$$g^n$$
thanks