711 ?
In how many ways can a dice be coloured with 6 different colours?
Means all the 6 faces should have 6 different colours. there are no other conditions..
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9 Answers
7Vivek, i hope u didn't think a lot for this sum. since most students who thought more got entangled and gave ans like ...............(including me)
262http://www.targetiit.com/iit-jee-forum/posts/painting-a-cube-20612.html
7But aditya , the ans is 1. since all the sides r identical. u can't distinguish each permutation with the other after painting the square since all will look identical after colouring.
21It is a 3-d closed loop that is why it may seem similar.
As an example consider two cases:
In both cases the base is coloured with white, and the opp. side with green in one case and blue in the other.
Now place the two arrangements on table with base in contact with table.Will they seem similar??
71Oh Yes.
For clearing confusion :
https://docs.google.com/viewer?a=v&q=cache:lKTmaEAL0ekJ:www.puzzles.com/puzzleplayground/PaintingACube/PaintingACubePrintPlay.pdf+painting+a+cube+with+6+different+colors&hl=en&gl=in&pid=bl&srcid=ADGEESijyJ2WXXxd3vgkp2CL95X2i2ro1K25jcj-wLjR0ink2ShGVPqdkXwc9GU_UEFRhoE_8xC9Kr0Fx61qhEHlmU7Xk9OsqH5AC5Z74vhToaoAfsYQnR-FyyTsc_Twc6-peVWppqMw&sig=AHIEtbTGqDbBfzyj-t3ZnSV3wg3iWy02DA
7@Aditya , Well the ans given in S.K.Goyal is 1. But, i assume the ans is wrong i assume....