Letters (probability)

the attachments in this post are quite large. I am reattaching as word documents.

The probability of A letter going to A envelop and B, C, and D in wrong

A going into right envelop is 1/4
B going into wrong envelop is 2/3 ( 1-1/3)
C going into wrong envelop is 1/2
D automatically will go into the wrong envelop 1

1/4*2/3*1/2*1 = 1/12 (multiplication because everything occurs at once)

Similarly the same procedure will follow for B, C & D and the result will also be the same

1/12+1/12+1/12+1/12 = 4/12 = 1/3.

Anybody, please find the flaw in my reasosning:

1. To make 1st letter with correct adress:
1/4*2/3*1/2*1 = 1/12

2. To make 2nd letter with correct adress:
3/4*1/3*1/2*1 = 1/8

3. To make 3rd letter with correct adress:
3/4*2/3*1/2*1 = 1/4

4. To make 4th letter with correct adress:
3/4*2/3*1/2*1 = 1/4

summ will be 17/24

4meonly wrote:Anybody, please find the flaw in my reasosning:

1. To make 1st letter with correct adress:
1/4*2/3*1/2*1 = 1/12

2. To make 2nd letter with correct adress:
3/4*1/3*1/2*1 = 1/8

3. To make 3rd letter with correct adress:
3/4*2/3*1/2*1 = 1/4

4. To make 4th letter with correct adress:
3/4*2/3*1/2*1 = 1/4

summ will be 17/24

The flaw is in 1 and multiplications in general
1 should be = 2/24

1 should be = 2/24

does not this mean that 2/24 = 1/12 ?