Olympiad workbook
- Exam
- Olympiad workbook
- Subject
- IOQM
- Chapter
- Permutation and Combination
Olympiad workbook · IOQM · Permutation and Combination
What is the number of triples (a, b, c) of positive integers such...
What is the number of triples of positive integers such that (i) and (ii) , 10 form the sides of a quadrilateral?
Correct answer
73
Step-by-step solution
| a | b | c |
|---|---|---|
| 1 | 2 | 8,9 |
| 1 | 3 | 7,8,9 |
| 1 | 4 | 6,7,8,9 |
| 1 | 5 | 6,7,8,9 |
| 1 | 6 | 7,8,9 |
| 1 | 7 | 8,9 |
| 1 | 8 | 9 |
| 2 | 3 | 6,7,8,9 |
| 2 | 4 | 5,6,7,8,9 |
| 2 | 5 | 6,7,8,9 |
| 2 | 6 | 7,8,9 |
| 2 | 7 | 8,9 |
| 2 | 8 | 9 |
| 3 | 4 | 5,6,7,8,9 |
| 3 | 5 | 6,7,8,9 |
| 3 | 6 | 7,8,9 |
| 3 | 7 | 8,9 |
| 3 | 8 | 9 |
| 4 | 5 | 6,7,8,9 |
| 4 | 6 | 7,8,9 |
| 4 | 7 | 8,9 |
| 4 | 8 | 9 |
| 5 | 6 | 7,8,9 |
| 5 | 7 | 8,9 |
| 5 | 8 | 9 |
| 6 | 7 | 8,9 |
| 6 | 8 | 9 |
| 7 | 8 | 9 |