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Of 12 possible books, you plan to take three with you on vacation. How many different collections of three books can you take?...

Question

Of 12 possible books, you plan to take three with you on vacation. How many different collections of three books can you take?

of 12 possible books, you plan to take three with you on vacation. How many different collections of three books can you take?


Answers

There are eight books in a box.There is space on a bookshelf for only three books. How many different three-book arrangements are possible?

The given question is supposed that there are five books that you might bring along to read on your vacation. Now we have to find, how many different ways can you decide which book to bring and you want to bring? At least one? So then I five factorial ways in which deacon? Yeah. Bring at least one book. So five factorial can be written as five multiplied by four, multiplied by three, multiplied by two, multiplied by one. After simply five, we get 1 20 so there are 1 20. It's.

All right, You have got a 12 c four. I want to see how many off your collections you can. How many different possible computer nation you can make. So court minus four is eight Victoria and then for Victoria. So let's look into that. That's perfect analogy. Yes, that's quit. They know it's for a boat in tonight.

Okay, so in this problem, you're going to read four books and you have 10 books to choose from. And the question asks in How many orders can you do that? And when you're talking about doing things in a particular order, then you want to use the permutation formula. So we're going to find 10 p for and according to our formula here, that would be 10 factorial divided by 10 minus four factorial. And when we simplify that, we get 10 factorial divided by six factorial. Now you probably have a factorial button in your calculator, and you probably also have a permutation button. But just in case you wanted to do this by hand, 10 factorial would be 10 times 9/10 8 times, seven times, six times, five times, four times, three times, two times one and six Factorial would be six times five times for times three times, two times one, and you can see that you can cancel the factors of 65 and so on all the way down. And what you have left is 10 times nine times eight times seven, and that works out to be 5040

This question. We can describe it. It's a bit show here. So we hand up box? Yeah. And he said the box. We have totally eight books here. So we were the book One Jew Book Tree. Look for book five books six, books seven and book eight. And now we want you put into this shelf on Dfars. This shelf here we have only three places on Lee. So 12 and three here and in escalate. How many different voice you do? Just trade books here. And then we born into this shell from your and the answer for this one will be This question here will be given to the, uh we choose three books from Ah Sant off a votes. Andi, Juris Fred isn't by notation. It will be the doesn't know Titian for this one will be from eight. We juiced three and this left us see here will be the minimum with Jews here. And my family we get is a ligature. Eight Pretoria divided by train. Victoria I ate ministry for Triaud and fought by Greta. The answer it could You ate choose three and acquitted of 56. And that would be the answer for this question here


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