Retrieving Smallest Nth Value Match Within a List

Problem:

Columns A & B contain matching pairs of numbers and letters.
Each number in column A may appear multiple times, on each occasion with a different corresponding letter.
We want to search the data and retrieve the letter corresponding to the nth match of specified numbers from column A. Column C specifies the number to search for, and column D specifies the particular match required.

Solution:

Use the INDEX, SMALL, IF, and ROW functions as shown in the following Array formula:
{=INDEX($B$2:$B$12,SMALL(IF($A$2:$A$12=C2,ROW($B$2:$B$12)-ROW($B$2)+1),D2))}

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