การเรียงสับเปลี่ยนของรูบิค

[computer]

ในวิกิพีเดียบอกว่า
"ลูกบาศก์ของรูบิค มีจำนวนรูปแบบการเรียงสลับเปลี่ยนที่แตกต่างกันทั้งหมด $8! \times 3^7 \times 12! \times 2^{10}$"
อยากจะทราบค่ะว่าคิดมาได้ยังไง
หรือถ้าใครใจดีช่วยแปลทีค่ะ http://en.wikipedia.org/wiki/Rubik%2...#Permutations:

The original (3×3×3) Rubik's Cube has eight corners and twelve edges. There are 8! (40,320) ways to arrange the corner cubes. Seven can be oriented independently, and the orientation of the eighth depends on the preceding seven, giving 37 (2,187) possibilities. There are 12!/2 (239,500,800) ways to arrange the edges, since an even permutation of the corners implies an even permutation of the edges as well. (When arrangements of centres are also permitted, as described below, the rule is that the combined arrangement of corners, edges, and centres must be an even permutation.) Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving 211 (2,048) possibilities.
${8! \times 3^7 \times (12!/2) \times 2^{11}} = 43,252,003,274,489,856,000$