Combinations

How many arm-wrestles will there be in the royal arm wrestling championship?

Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?

What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?

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

120 students sit an exam with 100 marks available. What is the smallest number of pairs that are awarded the same mark?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

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?

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...