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