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How many words can be formed, given $4(a,b,c,d)$ letters, and in each word from $4$ letters there must be at least two letters are the same? The position of the letter doesn't matter. The answer is $232,$ I don't know how to "attack" it.

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  • $\begingroup$ How long are the words? $\endgroup$ – almagest May 19 '16 at 20:16
  • $\begingroup$ 4 letters, forgot the add this. $\endgroup$ – Planet_Earth May 19 '16 at 20:16
  • $\begingroup$ What do you mean "position doesn't matter"? Is "abbc" and "abcb" equal? $\endgroup$ – Fred Yang May 19 '16 at 20:24
  • $\begingroup$ There are $4^4$ possible words in total. There are $4!=24$ words with no repeats. Hence $256-24=232$ with at least one repeat. $\endgroup$ – almagest May 19 '16 at 20:25
  • $\begingroup$ @almagest, give this as answer so I can mark it as best. $\endgroup$ – Planet_Earth May 19 '16 at 20:26
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There are $4^4=256$ possible words in total. There are $4!=24$ words with no repeats. Hence $256−24=232$ with at least one repeat.

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