Permutations of n objects taken r at a time

In a group of 6 people, how many ways can a president, vice president, and secretary be chosen?

A team of 5 basketball players must be selected from a squad of 12 players. How many different teams can be selected?

You are asked to form a 4 digit PIN for your bank account. If no digit can be repeated, how many different PINs can you make?

In a class of 20 students, a team of 5 students is to be formed for a school project. How many ways can the team be selected if the order in which the students are chosen doesn't matter?

How many permutations are possible if you arrange 8 people in a line, but one of them always demands to be at the front?

A student has to answer 5 questions out of 8 given questions. In how many ways can the student select the questions?

In a sports event, 7 teams are competing for the top 3 positions. How many different ways can the three positions be filled?

A password consists of 3 distinct digits followed by 2 distinct letters. How many different passwords can be made if digits and letters cannot be repeated within a password?

How many different four-letter codes can be formed from the English alphabet if no letter can be repeated?

In how many ways can a committee of 3 be formed from a group of 9 people?

How many ways can you arrange a 5 member committee from a group of 10 people?

If you have 7 books but only have space to display 4 on a shelf, how many different arrangements of those books can you have?

In a license plate number we have two letters and two numbers. The numbers must be different and the letters must be different. How many different license plate numbers can we make given that there are 26 letters in the English alphabet and digits ranging from 0 to 9?

In a race involving 8 athletes, how many ways can the first, second and third positions be filled?

A combination lock uses a 3 digit code, with digits from 0-9. Each digit can only be used once. How many distinct possibilities for the code are there?