NEED HELP URGENT! Probability Question
- Thread starter tenzdorj
- Start date
- Tags permutation probability question
The boys need to arranged like this:
_B_B_B_B_B_B_B_B_B_B_
and the remaining 15 girls have to go into the 11 blank spots. The first or last blank could be left empty, but there has to be at least one girl in each of the 9 blank spots between the boys
_BG_BG_BG_BG_BG_BG_BG_BG_BG_BG_
That leaves 6 girls that can go into any of the 11 spots.
The number of different ways to distribute n indistinguishable girls into k distinguishable spots is \({{n + k - 1}\choose{k - 1}}\)
\({{6 + 11 - 1}\choose{11 - 1}} = {{16}\choose{10}} = 8008\)
_B_B_B_B_B_B_B_B_B_B_
and the remaining 15 girls have to go into the 11 blank spots. The first or last blank could be left empty, but there has to be at least one girl in each of the 9 blank spots between the boys
_BG_BG_BG_BG_BG_BG_BG_BG_BG_BG_
That leaves 6 girls that can go into any of the 11 spots.
The number of different ways to distribute n indistinguishable girls into k distinguishable spots is \({{n + k - 1}\choose{k - 1}}\)
\({{6 + 11 - 1}\choose{11 - 1}} = {{16}\choose{10}} = 8008\)
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