Question 1205502
To express a permutation as a product of transpositions, we need to identify the pairs of elements that need to be swapped to transform the identity permutation into the given permutation.

**1. [1 2     3 4    3 4     5 6    5 6     8 2      7 8 7 1 ]**

We can break down this permutation into the following steps:

1. Swap 2 and 8: (2 8)
2. Swap 1 and 7: (1 7)
3. Swap 3 and 4: (3 4)
4. Swap 5 and 6: (5 6)

So, the permutation can be expressed as a product of transpositions:

```
(2 8)(1 7)(3 4)(5 6)
```

**2. [1 2     1 3     3 4     8 4     5 6     6 7      7 8 5 2 ]**

We can break down this permutation into the following steps:

1. Swap 2 and 3: (2 3)
2. Swap 4 and 8: (4 8)
3. Swap 6 and 7: (6 7)
4. Swap 5 and 2: (5 2)

So, the permutation can be expressed as a product of transpositions:

```
(5 2)(6 7)(4 8)(2 3)
```