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![]() Where 8!/(8-3)! is just a fancy way of saying “Use the first 3 numbers of 8!”. What’s another name for this? 5 factorial!Īnd why did we use the number 5? Because it was left over after we picked 3 medals from 8. This is where permutations get cool: notice how we want to get rid of $5 * 4 * 3 * 2 * 1$. Unfortunately, that does too much! We only want $8 * 7 * 6$. To do this, we started with all options (8) then took them away one at a time (7, then 6) until we ran out of medals. The total number of options was $8 * 7 * 6 = 336$. ![]() ![]() We picked certain people to win, but the details don’t matter: we had 8 choices at first, then 7, then 6. Silver medal: 7 choices: B C D E F G H.Gold medal: 8 choices: A B C D E F G H (Clever how I made the names match up with letters, eh?).We’re going to use permutations since the order we hand out these medals matters. How many ways can we award a 1st, 2nd and 3rd place prize among eight contestants? (Gold / Silver / Bronze) We’re using the fancy-pants term “permutation”, so we’re going to care about every last detail, including the order of each item. For instance, there are six different permutations of first, second, and third-place winners in the example above, but only a single combination of winners.Let’s start with permutations, or all possible ways of doing something. In most cases, there will be more possible permutations of objects in a set. If the top three winners were all given the same prize and who came in first is not important, then the winners could be considered a combination. The order of the winners is important because it’s important to know who came in first, second, and third. With combinations, the order is not relevant, and multiple permutations of the same items but in a different order are considered the same combination.Īn example of a permutation might be the top three winners of a race. Permutations are similar to combinations, but they are different because the order of the items in the sample is important. The number of possible permutations of r items in a set of n items with repetitions is equal to n to the power of r. The following formula defines the number of possible permutations of r items in a collection of n total items, allowing for repetitions: However, what if you want to consider that the words “ROT” and “ROT” using the different “O”s are different variations? The formula to calculate the number of permutations when allowing for repetitions in the sample is different. ![]() The permutations formula above will calculate the number of permutations without repetitions. ![]() If you want to find the number of three-letter words you can make using these five letters, you might consider that the duplicate “O”s do not form different words.įor instance, “ROT” and “ROT” using the different “O”s are the same word, so they would not be counted as separate permutations in this example. But in some cases, you may want to allow for the repetition of duplicate values.įor example, let’s say you have the letters “FOORT”. So far, the formulas to calculate permutations have not allowed any repetition in the sample, and the assumption has been that each element is unique. Thus the number of permutations of r items in a set of n items is equal to n factorial divided by n minus r factorial. The following formula defines the number of possible permutations of r items in a collection of n total items. Once you know the number of permutations of a set, you can calculate the probability of each one of them occurring. There is a formula to calculate the number of possible permutations of items in a set. The number of possible permutations for items in a set is often represented as nPr or k-permutations of n.Ī permutation is basically one possible way to represent a sample of items in a particular order from a large set. A permutation is a group of items from a larger set in a specific, linear order. ![]() ![]() Some may be living in a different time zone or have caring responsibilities that make it difficult for them to join the live session. For guidance on internet speed and video quality settings, see Panopto's guidance on choosing the best quality settings.Ĭonsider your viewers before asking them to join a live stream. Requires a high-speed internet connection. For interactive live sessions, video conferencing tools are more appropriate. Although viewers of the live stream can post comments in the video discussion, they cannot share their audio or video. With Panopto, only one person can stream and record audio and video. is not recommended for remote, interactive sessions (such as supervisions) that involve multiple participants speaking.Live streaming using the desktop recorder while recording a session The advantage of setting up a live stream in advance is that the Viewer URL link to the recording is pre-generated and can be shared with your students in Moodle along with the date and time of the session. in advance using the Panopto cloud dashboard.using the desktop recorder at the time of recording (this is the simplest and quickest way to set up a live stream using Panopto webcast).There is approximately a 30 to 45 second delay between your live stream and what the students will see, so questions and comments if enabled may seem a little behind.įor MLC, you can set up a live stream recording: ![]() Students will be able to comment on the live session and these can be seen in the Panopto personal recorder by you as the presenter. ![]() This will allow students to watch a live lecture or a demonstration remotely. ![]() Recordings in Panopto can be live-streamed (also known as webcasting) using the Webcast feature. ![]() |
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