EJU Japan · EJU Mathematics Course 1

Counting and Probability

26 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 26 questions

  1. A committee of 3 people is to be chosen from 8 volunteers. How many different committees are possible?
  2. A committee of 4 people is to be chosen from 11 volunteers. How many different committees are possible?
  3. A committee of 4 people is to be chosen from 7 volunteers. How many different committees are possible?
  4. How many 3-digit even numbers can be made from the digits 0, 1, 2, 3, 4 if no digit is used twice?
  5. A committee of 3 people is to be chosen from 12 volunteers. How many different committees are possible?
  6. A team has 4 men and 5 women. In how many ways can a group of 2 men and 2 women be chosen?
  7. A committee of 4 people is to be chosen from 6 volunteers. How many different committees are possible?
  8. A committee of 2 people is to be chosen from 12 volunteers. How many different committees are possible?
  9. A committee of 2 people is to be chosen from 11 volunteers. How many different committees are possible?
  10. In how many ways can 4 distinct prizes be given to 7 candidates, with no candidate receiving more than one prize?
  11. How many different arrangements of all the letters of the word CANDLE are there?
  12. How many different arrangements of all the letters of the word BANANA are there?
  13. A committee of 2 people is to be chosen from 9 volunteers. How many different committees are possible?
  14. A team has 7 men and 4 women. In how many ways can a group of 2 men and 1 women be chosen?
  15. In how many ways can 4 distinct prizes be given to 6 candidates, with no candidate receiving more than one prize?
  16. A committee of 2 people is to be chosen from 10 volunteers. How many different committees are possible?
  17. A fair coin is tossed 6 times. What is the probability of getting at least one head?
  18. Two fair dice are thrown. What is the probability that the sum of the numbers is 9?
  19. A fair coin is tossed 4 times. What is the probability of getting at least one head?
  20. A box has 5 red and 3 white marbles. Two marbles are taken out at the same time. What is the probability that both are red?
  21. A box has 6 red and 6 white marbles. Two marbles are taken out at the same time. What is the probability that both are red?
  22. Two fair dice are thrown. What is the probability that the sum of the numbers is 10?
  23. A fair coin is tossed 5 times. What is the probability of getting at least one head?
  24. A box has 3 red and 4 white marbles. Two marbles are taken out at the same time. What is the probability that both are red?
  25. A box has 3 red and 6 white marbles. Two marbles are taken out at the same time. What is the probability that both are red?
  26. A box has 6 red and 3 white marbles. Two marbles are taken out at the same time. What is the probability that both are red?

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