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The commander of space cruiser wishes port tour sentry ships arrayed around the cniser at the vertices of tetrahedron for defensive purposes since an attack can com...

Question

The commander of space cruiser wishes port tour sentry ships arrayed around the cniser at the vertices of tetrahedron for defensive purposes since an attack can come from any direction.(a) How many ways are there - deploy the ships if there are two different kinds of sentry ships available. and we discount all symmetries of the tetrahedral formation? (b) How many Ws are there if there are three different kinds of sentry ships available?

The commander of space cruiser wishes port tour sentry ships arrayed around the cniser at the vertices of tetrahedron for defensive purposes since an attack can come from any direction. (a) How many ways are there - deploy the ships if there are two different kinds of sentry ships available. and we discount all symmetries of the tetrahedral formation? (b) How many Ws are there if there are three different kinds of sentry ships available?



Answers

A convoy of 20 cargo ships and 5 escort vessels approaches the Suez Canal. In each scenario, how many different ways are there that these vessels could begin to go through the canal? a. A cargo ship and then an escort vessel b. A cargo ship or an escort vessel c. A cargo ship and then another cargo ship

So we have a setup that we have 20 different cargo ships, supposed to be a zero. Can we have five different tests or test missiles And we want to know how many different ways can we choose? Have a cargo go through. I believe it was the Suez Canal and then and fast forward. So there are 20 different Carlo ships which could go through and then there will be five different escorts. So there are 100 different ways for that to him. Now, what's the likelihood of a cargo ship going through or an escort? That's all? And in that case we have 20 different partnerships. Plus we have five different escorts. So there are 25 ways for that. Lastly, what's the likelihood that we have a cargo ship go through and then another cargo ship goes through? So we know there are 20 cargo ships And now one of them has gone through. So now there are only 19 months, two times 19 is 38, Sometimes time. So there are 380 ways for them to have

We know that a right cunt has an infinite number of planes. And then for part B with the Cube, you know, we have three planes. Parallels explains opposite. Therefore, three plus six would be nine planes on them for part C. We know that we have axes that connect Vergis is and then we have mid points. Therefore, we have three plus three plus one, so total we have seven axes of symmetry.

Now here on this problem, we're talking about shuffling a deck of cards. Now, in order to do this. It is important remember that In fact Toral is the number of ways to arrange in objects in a row. Yeah, This is helpful here because on a we want to know how many different ways can we shuffle a deck of 52 cards. Now, that's just the definition of 52 factory here. What's that means that a the number of ways to arrange 52 cards, It's just 52 factorial on P. We want to know how many different ways can we arrange the cards So that the four aces are on top. Now the four aces are on top. That means you have 48 other cards to arrange at the end, And there are 48 factorial ways that we can arrange them. Now, those four aces there in the beginning, we also need to look at how many ways we can arrange them, And there are four factorial ways we can arrange those aces in the beginning, and so the total number of ways of arranging the deck of cards in this order. As for factory all times 48 that or yeah.

Now here on this problem, we're talking about shuffling a deck of cards. Now, in order to do this. It is important remember that In fact Toral is the number of ways to arrange in objects in a row. Yeah, This is helpful here because on a we want to know how many different ways can we shuffle a deck of 52 cards? Now, that's just the definition of 52 factory all here. What's that means that a the number of ways to arrange 52 cards, It's just 52 factorial on P. We want to know how many different ways can we arrange the cards So that the four aces are on top. Now the four aces are on top. That means you have 48 other cards to arrange at the end And there are 48 factorial ways that we can arrange them. Now, those four aces there in the beginning, we also need to look at how many ways we can arrange them. And there are four factorial ways we can arrange those aces in the beginning, and so the total number of ways of arranging the deck of cards in this order. As for factory all times 48 that or yeah.


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