Seven little men

Discrete Mathematics Level 5

Seven little men live in a little cottage.

Their names are:

  • Dopey
  • Sneezy
  • Bashful
  • Doc
  • Sleepy
  • Grumpy
  • Happy

Outside are seven little stepping stones, each inscribed with one letter which corresponds to the first initial of each of the little men. i.e. They are inscribed with the letters D, S, B, D, S, G, and H.

How many different ways can they stand, one on each stepping stone, so that no one stands on a stepping stone with his first initial on it?

e.g. Dopey can't stand on either of the "D" stepping stones.

Note: Dwarves that have the same first initial are distinguishable, so, for example, if Dopey and Doc trade places, it's a different arrangement.

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