2021 RVHS J2 CT Q9

An ice-cream café sells a mega sundae in which the customer will order \(5\) scoops of ice-cream. The staff will arrange the \(5\) scoops on a plate in either a circular or row manner. The café offers exactly \(10\) distinct flavours of ice-cream daily

1. Find the number of ways the mega sundae can be arranged in a circular manner if \(5\) distinct flavours of ice- cream are to be chosen.[1]
2. A customer decides to order the vanilla, chocolate and banana flavour among the flavours for all \(5\) scoops of ice-cream but does not specify the number of scoops for each flavour, i.e., some flavour of ice-cream can have \(2\) or more scoops.
   Find the number of ways the staff can arrange the mega sundae in a row manner.[2]