![]() We could have that, or we could have that. The same three people, but we're putting them This would be countedĪs another permutation. And this would be countedĪs another permutation. When we're talking about permutations, we care about who's sitting in which chair. Now it's worth thinking about what permutations are counting. So your total number of scenarios, or your total number of permutations where we care who's sitting in which chair is six times five times four, which is equal to 120 permutations. So for each of these 30 scenarios, you have four people who you could put in chair number three. To have four people standing up not in chairs. And now if you want to say well what about for the three chairs? Well for each of these 30 scenarios, how many different people could you put in chair number three? Well you're still going So you have a total of 30 scenarios where you have seated six You have five scenarios for who's in chair number two. Someone in chair number one and for each of those six, Or another way to think about it is there's six scenarios of So that means you haveįive out of the six people left to sit in chair number two. Scenarios we've taken one of the six people to Now for each of those six scenarios, how many people, how many different people could sit in chair number two? Well each of those six There are six people whoĬould be in chair number one. We put in chair number one? Well there's six different And we can say look if no one's sat- If we haven't seated anyone yet, how many different people could Permutations of putting six different people into three chairs? Well, like we've seen before, we can start with the first chair. But it'll be very instructive as we move into a new concept. This is covered in the permutations video. One, chair number two and chair number three. Out all the scenarios, all the possibilities,Īll the permutations, all the ways that we could Video, we're going to say oh we want to figure Person B, we have person C, person D, person E, and we have person F. a.About different ways to sit multiple people in.In how many ways can all 7 letters of the word QUIETLY be arranged if the letters Q and U must be next to each other in the order QU?.How many different arrangements in a row are possible? There must be a bush at each end, and four flowering plants in a row in between the bushes. She needs to plant a row of 6 plants in a garden. A landscaper has 6 different flowering plants and 4 different non-flowering bushes.In how many orders could these 7 vehicles be listed in the auction program? At an auction of used construction vehicles, there are 7 different vehicles for sale.How many different ways can 4 of the 6 plants be arranged in a row? She needs to plant 4 of them in a row in a garden. A landscaper has 6 different flowering plants.In how many ways can 5 of the 9 fancy cakes be lined up in a row in the bakery display case? In how many ways can you put the books on the shelf if the first two slots are to be filled with the books of one subject and the next three slots are to be filled with the books of the other subject? You have 5 math books and 6 history books to put on a shelf with five slots.In how many ways can you put the books on the shelf if the first two slots are to be filled with math books and the next three with history books? In how many ways can 3 English, 3 history, and 2 math books be set on a shelf, if they are grouped by subject?.In how many ways can 3 English, 3 history, and 2 math books be set on a shelf, if the English books are set on the left, history books in the middle, and math books on the right?.In how many different ways can five people be seated in a row if two of them insist on not sitting next to each other?.In how many different ways can five people be seated in a row if two of them insist on sitting next to each other?.How many three-digit odd numbers are there?.How many three-digit numbers are there?.How many permutations of the letters PRODUCT have consonants in the second and third positions?.How many permutations of the letters of the word SECURITY end in a consonant?.How many permutations of the letters of the word PROBLEM end in a vowel?.In how many ways can the letters of the word CUPERTINO be arranged if each letter is used only once in each arrangement?.How many different ways can this be done? A group of fifteen people who are members of an investment club wish to choose a president, and a secretary.How many different ways can the 7 clerks be assigned to the 5 counters? A grocery store has five checkout counters, and seven clerks.
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