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2020©by the Society of Physical Therapy Science. Published by IPEC Inc.The main theme of this paper is the enumeration of the order-isomorphic occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence f r v ( k , n ) , the number of n-array k-ary words that contain a given pattern v exactly r times. In addition, we study the asymptotic behavior of the random variable Xn , the number of pattern occurrences in a random n-array word. The two topics are closely related through the identity