Mum has a new kitchen. There is a drawer for cutlery which is 80 cm across and 40 cm deep.
She has four rectangular trays that are each 20 cm by 40 cm that she can put into the drawer. The four trays are for knives, forks, spoons, and big utensils.
In how many different ways can Mum put the four rectangular trays into the drawer?
Solution
One way to do this is to cut out four pieces of paper (say 2cm by 4cm) and place these on to a larger rectangle (4cm by 8cm).
The four trays will fit if they are all vertical (up and down), and they will fit if they are horizontal (left to right). By moving the trays we can also have two going each way. If you play around you will find that the two that are horizontal can go on the left, on the right or in the middle.
So Mum can have 5 different possible arrangements of trays. We show each of these below.
Extension
What if Mum’s cutlery drawer was 40 cm by 60 cm? How many different ways could she put three trays in it?
What if Mum has a cutlery drawer that is 40cm by 100cm? How many different ways could she put five trays in it?