How many numbers greater than 5000 can be formed with four of the digits 3, 4, 5, 6, 7 where no digit can be repeated

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1. When none of the digits are repeated:

   The hundred’s place can be filled by any of the digits: 2, 3, 5, 6, 7 or 8 except the one which has already been used at the thousand’s place, so it can be filled in 5 ways.

   Similarly tens’ place can be filled in 4 ways: only those 4 numbers which have not been use either at hundred’s or thousand’s place.
   Unit’s place can be filled in only 3 ways. So, total number of nos. Possible =4×5×4×3= 240

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