There are 17 points on the circumference of a circle how many lines can be drawb to connect all possible pairs of points?
2 points make a straight line
so no of lines required=17C2=136
Well, I must say, those 17 points really know how to party! To answer your question, let's get creative. Imagine you're playing a game of connect-the-dots with these points. To connect any two points, we draw a line. So, the first point can be connected to the remaining 16 points, giving us 16 lines. The second point can be connected to the remaining 15 points (excluding the first one), resulting in 15 lines. We can continue this pattern until we reach the last two points, which can be connected with just one line.
Now, if we add up all those lines, we get 16 + 15 + 14 + ... + 1. But wait, there's a shortcut! This sum can be calculated using the formula for the sum of an arithmetic series: S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, n is 16, a is 16, and l is 1. Plugging in these values, we get:
S = (16/2)(16 + 1) = 8 * 17 = 136.
So, there you have it! 136 lines can be drawn to connect all possible pairs of points on that circle. Enjoy connecting those dots, and remember, even circles can have a sense of humor!
To determine the number of lines that can be drawn to connect all possible pairs of points on the circumference of a circle, you can use the formula:
Number of lines = (n * (n-1)) / 2
where "n" represents the number of points on the circumference.
In this case, you have 17 points on the circumference. Plugging this value into the formula:
Number of lines = (17 * (17-1)) / 2
= (17 * 16) / 2
= 272 / 2
= 136
Therefore, there can be 136 lines drawn to connect all possible pairs of points on the circumference of a circle with 17 points.
To calculate the number of lines that can be drawn to connect all possible pairs of points on the circumference of a circle, you can use the combination formula.
The combination formula calculates the number of ways to choose a certain number of items from a larger set, without regard to the order of the items.
In this case, you need to find the number of ways to choose 2 points out of the 17 points on the circumference of the circle.
You can use the combination formula:
C(n, r) = n! / (r!(n - r)!)
where C(n, r) represents the number of combinations of n items taken r at a time, and n! denotes the factorial of n.
Applying the formula to this problem, you have:
C(17, 2) = 17! / (2!(17 - 2)!)
Simplifying further:
C(17, 2) = 17! / (2! * 15!)
Note: 2! is equal to 2 factorial which is 2 * 1 = 2.
Now, you can calculate this expression using a calculator, or break down the factorials step by step:
17! = 17 * 16 * 15!
Plugging this back into the combination formula:
C(17, 2) = (17 * 16 * 15!) / (2 * 15!)
The 15! cancels out:
C(17, 2) = 17 * 16 / 2
Finally, calculating the expression:
C(17, 2) = 8 * 17 = 136
Therefore, there can be 136 lines drawn to connect all possible pairs of points on the circumference of a circle with 17 points.