Permutations – Fundamental Principle of Counting

Grade 11 Maths — Permutations – Fundamental Principle of Counting: 25 practice questions with instant scoring and explanations.

1. The fundamental principle of counting states:
2. A person has 3 shirts and 2 pairs of pants. Total ways to dress are:
3. From city A to B there are 4 routes, and B to C there are 3 routes. Total ways from A to C via B:
4. A number plate has 2 letters followed by 3 digits. Total possible plates (26 letters, 10 digits):
5. How many 2-digit numbers can be formed from digits {1, 2, 3, 4}?
6. A coin is flipped 3 times. Total possible outcomes:
7. A die is rolled and then a coin is flipped. Total outcomes:
8. From 5 cities, a traveler must visit 3 cities in sequence (no repetition). Ways to do so:
9. How many 3-digit numbers can be formed from {1, 2, 3, 4, 5} with repetition?
10. How many 3-digit numbers can be formed from {1, 2, 3, 4, 5} without repetition?
11. A password has 2 letters (26 choices) and 2 digits (10 choices). Total passwords:
12. Ways to arrange 3 distinct books on a shelf:
13. Ways to choose a president, vice-president from 5 people:
14. A menu has 3 appetizers, 4 mains, 2 desserts. Ways to choose one of each:
15. How many ways can we fill 3 positions with 6 people (no repetition)?
16. A lock has 4 dials, each with 10 digits. Total combinations:
17. Ways to select 3 students from 5 to sit in a row (order matters):
18. A flag has 3 stripes of different colors. Colors available: 5. Ways to color:
19. An exam has 10 questions with 4 choices each. Total ways to answer all:
20. How many ways to arrange 5 people in a line?
21. Ways to make 3-letter codes from 26 letters (with repetition):
22. A committee of 1 president and 1 secretary from 8 people. Ways to form:
23. How many 4-letter words (using English alphabet, with repetition)?
24. Number of ways to arrange the letters of CAT:
25. Total 2-digit numbers (first digit 1-9, second digit 0-9):