36 identical chairs must be arranged in rows with the same number of chairs in each row.  Each row must contain at least 3 chairs and there must be at least 3 rows.  A row is parallel to the front of the room.  How many different arrangements are possible?

A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?

In a certain laboratory, chemicals are identified by a colour-coding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique two-colour pair. If the order of colours in the pairs does not matter, what is the minimum number of different colours needed to code all 20 chemicals with either a single colour or a unique pair of colours?