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1. Suppose there are 10 points in a plane such that no three points are collinear. How many distinct triangles can be found with 3 of these points as vertices?

1. Suppose there are 10 points in a plane such that no three points are collinear. How many distinct triangles can be found with 3 of these points as vertices?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Mathematical Problem Solving Exercise** **C. Solve the following problems:** 1. **Triangular Formations on a Plane:** Suppose there are 10 points in a plane such that no three points are collinear. How many distinct triangles can be found with 3 of these points as vertices? 2. **Formation of Study Groups:** From a class of 32 girls and 18 boys, how many study groups of 3 girls and 2 boys can be formed? 3. **Forming a Committee:** A five-member committee is being formed from a group of 9 sophomores and 12 seniors. How many committees can be formed given each condition? - a. All sophomores - b. All seniors - c. 1 sophomore, 4 seniors - d. 3 sophomores, 2 seniors 4. **Choosing Friends for a Trip:** Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how many ways can they be chosen?
Transcribed Image Text:**Mathematical Problem Solving Exercise** **C. Solve the following problems:** 1. **Triangular Formations on a Plane:** Suppose there are 10 points in a plane such that no three points are collinear. How many distinct triangles can be found with 3 of these points as vertices? 2. **Formation of Study Groups:** From a class of 32 girls and 18 boys, how many study groups of 3 girls and 2 boys can be formed? 3. **Forming a Committee:** A five-member committee is being formed from a group of 9 sophomores and 12 seniors. How many committees can be formed given each condition? - a. All sophomores - b. All seniors - c. 1 sophomore, 4 seniors - d. 3 sophomores, 2 seniors 4. **Choosing Friends for a Trip:** Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how many ways can they be chosen?
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