The deck in Hope's backyard is round. It has 5 posts evenly spaced around the edge to support a trellis. For her birthday party, she wants to connect each post to all the other posts with crepe-paper streamers. How many streamers will she report?
Each post is connected to 4 others. Since each streamer connects in both directions, you don't want to count them twice, so you have
5*4/2 = 10 streamers
To find out how many streamers Hope will need to connect each post to all the other posts, we can use a combination formula.
Since there are 5 posts evenly spaced around the edge of the round deck, we can assume that each post needs to be connected to the other 4 posts.
To calculate the number of streamers, we need to find the number of combinations of 5 posts taken 2 at a time (since each streamer connects 2 posts).
The combination formula is:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items chosen at a time.
Applying the combination formula, we have:
C(5, 2) = 5! / (2!(5-2)!)
= (5 * 4 * 3 * 2 * 1) / ((2 * 1) * (3 * 2 * 1))
= 10
Therefore, Hope will need 10 streamers to connect each post to all the other posts.