Permutations & Combinations – Mixed Problems, Division & Distribution

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

1. In how many ways can 12 identical balls be distributed among 4 distinct boxes?
2. The number of ways to distribute n identical objects into r distinct groups is:
3. In how many ways can 8 distinct objects be divided into groups of 3, 3, and 2?
4. A student must solve exactly 5 problems from 8 given problems. In how many ways can this be done?
5. The number of ways to select r objects from n objects where order matters is:
6. How many ways can 10 different objects be distributed among 3 people such that one gets 5, one gets 3, and one gets 2?
7. In how many ways can 6 identical balls be placed into 3 distinct boxes with no box empty?
8. The number of ways to choose 2 red balls from 5 red and 3 white balls and 1 white ball is:
9. How many 4-digit numbers can be formed using digits 1-9 where digits must be distinct and number is divisible by 5?
10. In how many ways can 9 identical objects be distributed among 4 distinct boxes?
11. The number of solutions to x + y + z = 15 where x, y, z are non-negative integers is:
12. How many ways can 5 boys and 3 girls stand in a line such that no two girls are adjacent?
13. In how many ways can the letters of ACCOUNTANT be arranged such that vowels are together?
14. The number of ways to arrange 7 objects in a line such that 2 specific objects are not adjacent:
15. How many ways can 3 prizes be distributed among 7 students if a student can receive more than one prize?
16. In how many ways can r objects be selected from n objects where repetition is allowed?
17. The number of non-negative integer solutions to x + y + z + w = 8 is:
18. How many 3-digit numbers can be formed using 0, 1, 2, 3, 4, 5 without repetition?
19. The number of ways to divide 10 identical objects into 4 groups is:
20. In how many ways can 8 books be selected from 10 books such that 2 specific books are always excluded?
21. The number of positive integer solutions to x + y + z = 12 is:
22. How many ways can 5 different books be distributed to 3 children such that each child gets at least one book?
23. The number of permutations of the word BANANA is:
24. In how many ways can 20 identical coins be distributed among 4 different children?
25. In how many ways can 6 distinct objects be divided equally into 3 groups?