Combinations – nCr, Properties, Applications

Grade 11 Maths Higher — Combinations – nCr, Properties, Applications: 25 practice questions with instant scoring and explanations.

1. nCr is defined as:
2. Using the standard identity, the value of 5C3 is:
3. Using the standard identity, the value of 8C6 is:
4. The property nC0 + nC1 + nC2 + ... + nCn equals:
5. nCr = nC(n-r) is:
6. Using the standard identity, the value of 10C1 is:
7. Using the standard identity, the value of nCn is:
8. How many ways can 5 cards be selected from a deck of 52?
9. From 8 people, in how many ways can a committee of 3 be formed?
10. Using the standard identity, the value of 10C7 is:
11. The number of ways to select 2 red balls from 5 red and 3 blue balls is:
12. How many lines can be formed using 6 points where no three are collinear?
13. The number of diagonals in a pentagon is:
14. From 7 men and 4 women, how many committees of 5 people with 3 men and 2 women can be formed?
15. Using the standard identity, the value of 12C4 is:
16. The number of ways to choose 3 items from 10 different items is:
17. How many 4-person teams can be selected from 10 people?
18. Using the standard identity, the value of 6C3 + 6C4 is:
19. In how many ways can 6 prizes be distributed to 4 students with each getting at least one prize?
20. The relationship nCr + nC(r+1) = (n+1)C(r+1) is:
21. How many triangles can be formed using 10 points where no three are collinear?
22. From a group of 4 boys and 5 girls, how many committees of 5 with at least 2 girls can be formed?
23. If nCr = nCp, then r and p are related by:
24. Using the standard identity, the value of 15C14 is:
25. From 6 boys and 4 girls, how many committees of 4 can be formed?