(i)[4]
How many different selections are possible if there are no more than $3$ mountain bicycles and no more than $2$ of each of the other bicycle types?
(ii)[3]
How many different arrangements are there in the cycle rack if the mountain bicycles are all adjacent with no gaps between them, the ordinary bicycles are both adjacent with no gaps between them and all the spaces are adjacent?
(iii)[3]
How many different arrangements are there in the cycle rack if the ordinary bicycles are at each end of the bicycles and there are no spaces between any of the bicycles?