There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
In a certain city houses had to be built in a particular way.
There had to be two rooms on the ground floor and all other rooms had to be built on top of these.
Families were allowed to build just one room for each person living in the house.
So a house for two people would look like this:
but a house for three people could look like one of these:
There are some families of seven people living in the town.
In how many different ways can they build their houses?