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Who is older?

Question

Fifty school children lined up at random in five rows and ten columns.

No two of the children have the same birthday.

Of the oldest children in each column Pete is the youngest.

Of the youngest children in each row Jane in the oldest.

What is the probability that Pete is older than Jane?

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Let's call Wilhelm the kid

- in the same column as Pete (Pete is older than Wilhelm)

AND
- in the same row as Jane (Wilhelm is older than Jane)

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