Permutations & Combinations – Mixed Problems

Grade 11 Maths — Permutations & Combinations – Mixed Problems: 25 practice questions with instant scoring and explanations.

1. In how many ways can 4 boys and 3 girls be arranged in a row?
2. Number of ways to choose a committee of 3 from 5 men and 4 women:
3. Number of ways to arrange the word ARRANGE (with 2 R's and 2 A's):
4. From 5 English and 3 Maths books, ways to choose 2 English and 1 Maths:
5. If P(n, r) / C(n, r) = 24, then r! equals:
6. Number of ways to seat 5 men and 4 women in a row such that no two women sit together:
7. Ways to choose 3 consonants from {B, C, D, F, G} and 2 vowels from {A, E, I}:
8. Number of ways to distribute 10 identical items to 3 distinct people:
9. From a group of 7 people, select a president and a committee of 3 (president not in committee):
10. Number of 5-digit numbers with distinct digits from {1, 2, 3, 4, 5, 6, 7}:
11. Ways to select 3 cards from a deck of 52 (order matters):
12. Number of ways to arrange 3 red, 2 blue, 1 green balls in a row:
13. From 8 people, select 2 for a duet (order doesn't matter):
14. Number of subsets of a set with n elements:
15. Ways to choose president, vice-president, and treasurer from 10 people:
16. Number of ways to select 2 items from 6 items where order matters:
17. Ways to distribute 5 distinct gifts to 3 distinct children:
18. Number of permutations of {A, B, C, D} taken 2 at a time:
19. From 10 people, ways to form a committee of 4 without any restriction:
20. Number of ways to choose 5 cards from a deck keeping order:
21. Ways to arrange 2 identical red and 3 identical blue balls:
22. From 6 books, select 3 and arrange them on a shelf:
23. Number of ways to choose 2 red balls from 5 and 1 blue from 3:
24. If C(n, 2) = 21 and C(n, 3) = 35, then n equals:
25. Number of 4-digit numbers where all digits are different: