Tessellate S.T.E.M.S - Mathematics - School - Set 3 - Problem 5

25 25 identical balls are put in 25 25 boxes. All the distinct arrangements are given to be equally likely.

Given that after putting all the balls in boxes, at least one box is empty, what is the probability that exactly one box is empty?


This problem is a part of Tessellate S.T.E.M.S.

25 × 24 ( 50 25 ) \dfrac{25\times 24}{\binom{50}{25}} 25 × 24 ( 49 25 ) 1 \dfrac{25\times 24}{\binom{49}{25}-1} 25 × 24 2 5 25 \dfrac{25\times 24}{25^{25}} 25 × 24 1 ( 49 25 ) + 1 \dfrac{25\times 24 - 1}{\binom{49}{25}+1}

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