Problem B. 4722. (May 2015)
B. 4722. Each permutation of an \(\displaystyle n\)element set is coloured in either red, white or green. Let \(\displaystyle N_{\rm RWG}\) denote the number of ways to perform a red permutation followed by a white permutation and then a green permutation, such that each element is restored to its initial position at the end. Analogously, let \(\displaystyle N_{\rm GWR}\) denote the number of ways to perform a green permutation followed by a white permutation and then finally a red permutation, such that each element is restored to its initial position. Show that \(\displaystyle N_{\rm RWG}=N_{\rm GWR}\).
(6 pont)
Deadline expired on 10 June 2015.
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