the deck in hope's backyard is round. It has 5 posts evenly spaced around the edges to support a trellis. For her birthday party, shewants to connect each post to all the other posts with crepe-paper streamers.How many streamers will she need?
What is the perimeter of the deck? How long are the streamers?
That is all the information they give in the problem..
So your posts would form a pentagon.
The question becomes ....
How many sides and diagonals does a pentagon have?
There are 5 sides, and 5 diagonals (make a sketch to see how)
total streamers = 10
If you know combinations, this would be C(5,2) = 10
To determine how many streamers Hope will need to connect each post to all the other posts, we can use combinatorics, specifically the concept of combinations.
Since there are 5 posts, we need to choose 2 posts at a time to connect with a streamer. This is because we need to pick a starting post and an ending post for each streamer. In combinatorics, choosing 2 items from a set is represented by the notation "C(n, r)" or "nCr," where n is the total number of items and r is the number of items chosen.
In this case, since we have 5 posts and we need to choose 2 at a time, we can calculate the number of combinations using the formula:
nCr = n! / (r!(n - r)!)
Using the formula, we can calculate the number of combinations of choosing 2 posts out of the 5:
5C2 = 5! / (2!(5 - 2)!)
= (5 * 4 * 3!) / (2 * 1 * 3!)
= (5 * 4) / (2 * 1)
= 10
Therefore, Hope will need 10 streamers to connect each post to all the other posts in her backyard deck.