## Problem of the Day #134: Pasture Picking Parade
*July 31, 2011*

*Posted by Saketh in : potd , trackback*

Farmer John has $10$ cows on his farm, conveniently labeled from $1$ to $10$. After being milked each morning, the cows are led single-file in order along a path that passes each of $10$ pastures exactly once.

Before leaving the barn, each cow decides which pasture she wishes to graze in. When she reaches that pasture, she will try to occupy it for the day. If she finds that her desired pasture is already occupied, she will take the next available pasture she encounters (if there is one).

Determine the number of distinct mappings of cows to desired pastures for which all of the cows will find a place to graze.

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