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Ways to arrange dots and dividers #
What I struggle with is this. I don't know how many ways to arrange sticks and stones, when there is a maximum amount of stones to be arranged between sticks.
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In how many ways can we: nCk {0,1,2,3}
n integers 0 to n-1
width: places
∑
$P(A_1 + A_2 + A_3 + A_4) = P(A_4)^2$
1 0 1 1 0
2 $3\choose2$ {0,1} :: 1331 011 101 110
2 $3\choose1$ {0,1,2} :: 1331 11 20 02 3 {0,1,2,3} 4C2 ::: $1 4 6 4 1$ 30 03 12 21
Possible pairs adding up to 5: (1, 4), (2, 3), (3, 2), (4, 1)
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