Permutations

Which of these games would you play to give yourself the best possible chance of winning a prize?

How many six digit numbers are there which DO NOT contain a 5?

Seventh challenge cipher

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

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?

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 ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand corner of the grid?

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?