Combinations

How many 10-digit numbers containing only 1s, 2s and 3s can you write?

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Using only the red and white rods, how many different ways are there to make up the other rods?

Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?