How many ways are there to put 6 b***s in 3 boxes if three b***s are indistinguishably white, three are indistinguishably black, and the boxes are distinguishable?
+118703 DIFFERENT BOXES - 3 WHITE AND 3 BLACK B***S.
0,0,6 3*1=3 choice
0,1,5 3!* the 1 could but black or white 6*2=12 choices
0,2,4 3!*the 2 could be BB, WW or BW 6*3 = 18 choices
0,3,3 3* the 3 could be BBB, BBW, BWW or WWW but 2 of these are the same so 2 choices
(BBB,WWW) or (BBW)(WWB) 3*2= 6 choices
1,1,4 3* the ones can be BB, WW or BW 3*3 = 9 choices
1,2,3 3!*
If the first box has a B then the second can have BB, BW or WW
If the first box has a W then the second can have BB, BW or WW 6*6= 18 choices
2,2,2 1* If one box has WW then the other boxes must be BB and BW.
or BW,BW, BW 1*2= 2 choices
3+12+18+6+9+18+2=68
There is no guarantees that this is correct.
+118703 How many ways are there to put 6 b***s in 3 boxes if three b***s are indistinguishably white, three are indistinguishably black, and the boxes are distinguishable?
AGAIN i HAVE ANSWERED A DIFFERENT QUESTION HERE.
THIS IS BOXES ALL THE SAME, 3 BLACK AND 3 WHITE B***S
Again I am basing this one my original answer - if it its wrong then they are all wrong
0,0,6 1 choice
0,1,5 the 1 could but black or white 2 choices
0,2,4 the 2 could be BB, WW or BW 3 choices
0,3,3 the 3 could be BBB, BBW, BWW or WWW but 2 of these are the same so 2 choices
(BBB,WWW) or (BBW)(WWB)
1,1,4 the ones can be BB, WW or BW 3 choices
1,2,3 Now it is getting harder
If the first box has a B then the second can have BB, BW or WW
If the first box has a W then the second can have BB, BW or WW 6 choices
2,2,2 If one box has WW then the other boxes must be BB and BW.
or BW,BW, BW 2 choices
I hope I have got them all :/
1+2+3+2+3+6+2 = 19 possibilities
+118703 DIFFERENT BOXES - 3 WHITE AND 3 BLACK B***S.
0,0,6 3*1=3 choice
0,1,5 3!* the 1 could but black or white 6*2=12 choices
0,2,4 3!*the 2 could be BB, WW or BW 6*3 = 18 choices
0,3,3 3* the 3 could be BBB, BBW, BWW or WWW but 2 of these are the same so 2 choices
(BBB,WWW) or (BBW)(WWB) 3*2= 6 choices
1,1,4 3* the ones can be BB, WW or BW 3*3 = 9 choices
1,2,3 3!*
If the first box has a B then the second can have BB, BW or WW
If the first box has a W then the second can have BB, BW or WW 6*6= 18 choices
2,2,2 1* If one box has WW then the other boxes must be BB and BW.
or BW,BW, BW 1*2= 2 choices
3+12+18+6+9+18+2=68
There is no guarantees that this is correct.
