Permutations and Combinations

In how many ways can five people sit on a row of five chairs?

A set of eight cards each have a different colour. The cards are shuffled randomly

and then laid out in a line. How many different arrangements are possible?

In how many ways can ten people sit on a row of ten chairs?

In a race with eight competitors how many ways can the gold, silver and bronze medals be awarded?

How many different four-digit numbers can be made using the digits 1 to 9 at most once each?

How man different five-letter arrangements can be made usin the letters in CAMBRIDGE.

A set of eight cards each have a different color.

They are shuffled randomly and then three of them are laid out in a line.

How many different arrangements are possible?

A candidate in an examination has to answer four questions from a choice of six, and can answer them in any order.

How many different orders can the candidate provide their answers in?

There are six people including a husband and wife, and a row of six chairs.

In how many ways can the six people sit with no constraints?

There are six people including a husband and wife, and a row of six chairs.

In how many ways can they sit if the husband and wife are to sit together?