Four soccer players, three tennis players, two badminton players, and one swimmer sit at a round tab

Question

Four soccer players, three tennis players, two badminton players, and one swimmer sit at a round table with $10$ seats. Find the number of possible seating arrangements if the two badminton players sit together,[2] if the two badminton players sit directly opposite each other,[2] if the two badminton players sit together and none of the four soccer players sit next to either of the two badminton players,[2] if the two people sitting beside the swimmer are from different sports.[2]

Accepted Answer

(i) $80640$ (ii) $40320$ (iii) $17280$ (iv) $262080$

2010 NYJC P2 Q8

2010 NYJC P2 Q8

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