. Exercise: Answer the following.show your complete solution/s for each item.
1. Evaluate nCr =.3 points
2. How many ways are there in forming triangles from 6 distinct points in which number 3 points are collinear. 3 points
3. In how many ways can a committee of5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors? 6 points
4. How many possible ways can you choose four delegates from a class of 15 students to represent the school in another school's reference? 3 points
1. Evaluate nCr =.3 points
2. How many ways are there in forming triangles from 6 distinct points in which number 3 points are collinear. 3 points
3. In how many ways can a committee of5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors? 6 points
4. How many possible ways can you choose four delegates from a class of 15 students to represent the school in another school's reference? 3 points
Answers & Comments
Answer
1. nCr (n choose r) is a mathematical formula that gives the number of possible combinations of a set of n items taken r at a time. It is calculated as nCr = n! / (r! (n-r)!). In this case, we need more information such as n and r to evaluate the expression.
2. There are 6 distinct points and we need to form triangles from these points. To form a triangle, we need 3 points. When 3 points are collinear, they do not form a triangle. So, the number of ways to form triangles from 6 distinct points in which 3 points are collinear is 0.
3. In forming a committee of 5, we need to choose 5 people from a group of 5 juniors and 7 seniors, with 3 of the 5 people being seniors. The number of ways to choose 3 seniors from the 7 seniors is 7C3 = 7! / (3! (7-3)!) = 35. The number of ways to choose 2 juniors from the 5 juniors is 5C2 = 5! / (2! (5-2)!) = 10. The total number of ways to form a committee of 5 with 3 seniors and 2 juniors is 35 x 10 = 350.
4. In choosing 4 delegates from a class of 15 students, the number of possible ways is 15C4 = 15! / (4! (15-4)!) = 3003.
I hope these solutions are helpful