How many different collections of 9 letters are there? A letter can appear multiple times in a collection. Two collections are equal if each letter appears the same number of times in both collections.
Solution
We put these collections in bijections with binary strings of length 34 containing 9 zeroes and 25 ones. Take any such string - the 9 zeroes will correspond to the 9 letters in the collection. If there are ones before a zero, then that zero corresponds to the st letter of the alphabet. This scheme is an injective map from the binary strings to the collections, and it has an inverse, so the number of collections is .
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