Solve only problem (d) 3.3.4 It is clear that STATUS and LETTER have the same nu

Question

Solve only problem (d)

3.3.4 It is clear that STATUS and LETTER have the same number of anagrams (in fact, 6!/(2!2!) = 180). We say that these words are essentially the same (at least as far as counting anagrams goes): They have two letters repeated twice and two letters occurring only once. We call two words essentially different, if they are not essentially the same. (a) How many 6-letter words are there, if, to begin with, we consider any two words different if they are not completely identical? (As before, the words don't have to be meaningful. The alphabet has 26 letters.) (b) How many words with 6 letters are essentially the same as the word LETTER? (c) How many essentially different 6-letter words are there? (d) Try to find a general answer to question (c) (that is, how many essentially different words are there with n letters?). If you can't find the answer, read the following section and return to this exercise afterwards.

Explanation / Answer

d.)

No. of "essentially same" words of length n = (26Cn-2)* (nC2)* { (n!) / [(2!)(2!)] } = (26Cn-2)* (nC2)* (n!) / 4

No. of "essentially different" words of length n =26n - No. of "essentially same" words of length n

= 26n - (26Cn-2)* (nC2)* (n!) / 4

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