A $3 \times 3 \times 4$ cuboid is constructed out of 36 white-coloured unit cubes. Then, all six of the cuboid's sides are coloured red. After that, the cuboid is dismantled into its constituent unit cubes. Then, randomly, all said unit cubes are constructed into the cuboid of its original size (and position). a) How many ways are there to position eight of its corner cubes so that the apparent sides of eight corner cubes are still red? (Cube rotations are still considered distinct configurations, and the position of the cuboid remains unchanged.) b) Determine the probability that after the reconstruction, all of its apparent sides are still red-coloured. (The cuboid is still upright, with the same dimensions as the original cuboid, without rotation.)

HIDE: Notes The problem might have multiple interpretations. We agreed that this problem's wording was a bit ambiguous. Here's the original Indonesian version: Suatu balok berukuran $3 \times 3 \times 4$ tersusun dari 36 kubus satuan berwarna putih. Kemudian keenam permukaan balok diwarnai merah. Setelah itu, balok yang tersusun dari kubus-kubus satuan tersebut dibongkar. Kemudian, secara acak, semua kubus satuan disusun lagi menjadi balok seperti balok semula. a) Ada berapa cara menempatkan kedelapan kubus satuan yang berasal dari pojok sehingga kedelapan kubus di pojok yang tampak tetap berwarna merah? (Rotasi kubus dianggap konfigurasi yang berbeda, namun posisi balok tidak diubah.) b) Tentukan probabilitas balok yang tersusun lagi semua permukaannya berwarna merah. (Balok tegak tetap tegak dan balok tetap dalam suatu posisi.)