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In how many ways we can put $r$ distinct objects into $n$ baskets?
I have a doubt in following Combinatorics question : There are N bags, and there several balls of 4 colors (R,G,B,Y).Each bag should be filled by exactly one ball with the following condition -
-The color of ball in the consecutive bags must be different.
-The color of ball in first and last must be distinct too.
How many ways are there?
For N=2:
B-1|B-2
R G
R B
R Y
G R
G B
G Y
B R
B G
B Y
Y R
Y G
Y B
For N=3
B-1 B-2 B-3
R G B
R G Y
R B G
R B Y
R Y G
R Y B
G R B
G R Y
G B R
G B Y
G Y R
G Y B
B R G
B R Y
B G R
B G Y
B Y R
B Y G
Y R G
Y R B
Y G R
Y G B
Y B R
Y B G