Short, but is it Sweet?

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In how many ways can you permute four 1's and fifty 2's such that at least five 2's lie between each pair of 1's?

The answer is 82251.

1 solution

Brian Charlesworth
Oct 22, 2014

After placing $5$ $2$ 's in each of the $3$ gaps between the $4$ $1$ 's, we have $35$ $2$ 's left to place, in any combination, in the $5$ available positions, namely before the first $1$ , in the $3$ gaps between the $1$ 's, and after the last $1$ . This is a 'stars and bars' calculation with solution $\dbinom{35 + 5 - 1}{35} = \boxed{82251}$ combinations.

Short, but is it Sweet?

The answer is 82251.

1 solution

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