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 June 10, 2015.
Statistics:
7 students sent a solution. 6 points: Fekete Panna, Gáspár Attila, Glasznova Maja, Szebellédi Márton, Williams Kada. 3 points: 1 student. 0 point: 1 student.
Problems in Mathematics of KöMaL, May 2015