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Question
By using the digits 3,5,5,6,7,7,9 any number of times how many numbers can be formed having four digits?

Answer
You are not stating it clearly, so I will assume you mean:

By using the digits 3,5,5,6,7,7,9 how many four-digit numbers can be formed?

This is just 'Permutations with repeated elements.' and the answer should be:
  7|         << 7 possibilities
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2| 2!        << 2 identical 5's, and 2 identical 7's  

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