Combinations

WS#1G9
  1. In a game, there are 10 players, and the coach needs to choose a captain and a vice-captain. How many different combinations of captain and vice-captain are possible?

  2. A school has 5 different clubs, and each student can join only one club. If there are 25 students in the school, how many different ways are there for the students to join the clubs?
  3. In a pizza place, there are 8 different toppings available. If a customer wants to order a pizza with exactly 3 different toppings, how many different combinations of toppings are possible?

  4. A lock has 4 dials, each with digits from 0 to 9. If the lock code consists of 4 different digits, how many different combinations are possible?

  5. A teacher wants to assign a group project to 4 students out of a class of 25. How many different combinations of groups can be formed?

  6. A password consists of exactly 6 characters, where each character is either an uppercase letter (A-Z) or a digit (0-9). How many different passwords are possible?

  7. A committee of 5 members needs to be formed from a group of 12 people. If one of the members must be selected as the chairperson, how many different combinations of the committee and chairperson are possible?