Combinations

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours?

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

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.