the deck in hopes's backyard is round. it has 5 posts evently spaced around the edge to support a trellis. for her birthday party, she wants to connect each post to all the others post with crepe-paper streamers. how many streamers will she need?
An easy way to get this answer, which will also enable you to figure it for any number of posts, is to consider each post.
Connect the first post to each of the others. There are 4 streamers (to posts 2,3,4,5). Now, go to post #2. It still has to be connect to 3 posts (3,4,5). Then, on to post #3. It still needs streamers to 2 posts (4,5). On to post #4. It still needs 1 streamer, to post 5. By this time, post #5 has been connected to each of the other posts.
So, adding up all the streamers, we get 4+3+2+1 = 10.
So, you can see that for N posts, you will need (N-1)+(N-2)+...+2+1 streamers. Adding up all these numbers, you get N(N-1)/2.
Answers
To calculate the number of streamers needed to connect each post to all the others, we can use a combination formula.
The formula for calculating the number of combinations of k items taken from a set of n items is given by:
C(n, k) = n! / (k! * (n - k)!)
In this case, there are 5 posts (n = 5), and she wants to connect each post to all the others (k = 2). Since the order of the posts doesn't matter, we can use combinations.
C(5, 2) = 5! / (2! * (5 - 2)!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / (2 * 1)
= 10
Therefore, Hope will need 10 streamers to connect each post to all the others.
To find out how many streamers Hopes will need to connect each post to all the other posts, we can use a combination formula. The combination formula allows us to calculate the number of unique combinations possible given a certain number of items.
In this case, Hopes has 5 posts evenly spaced around the deck. Let's label the posts as A, B, C, D, and E. To connect each post to all the others, we need to find the number of unique combinations of 2 posts from a set of 5. Using the combination formula, we can calculate this as:
C(5, 2) = 5! / (2!(5-2)!) = 10
So, Hopes will need 10 streamers to connect each post to all the others.