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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 points)

Deadline expired on 10 June 2015.

Statistics on problem B. 4722.
 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

•  Támogatóink: Morgan Stanley