Seven little men live in a little cottage.
Their names are:
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.
More permutations problems
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This is just like this problem, but the difference is the dwarves are distinguishable, while the letters in GOOFING are not. Therefore, we need to multiply the answer by 4 . (Two for each set of distinguishable dwarves with the same initial letter in their name). Therefore the answer is 4 ∗ 2 3 0 = 9 2 0