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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 ...

Question

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?(Check your book to see image)a. A cargo ship and then an escort vesselb. A cargo ship or an escort vesselc. A cargo ship and then another cargo ship

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? (Check your book to see image) 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



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? (Check your book to see image) 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

Okay, This question is gonna ask us about the number of different ways we could get certain poker hands. And really, we just need to know that a poker hand is formed from any five cards in a normal day. So the 1st 1 asks, How many ways could we get a poker hand with four queens in it? So this is equal to the number of ways to get the Queen's times the number of ways to get everything else. So with the four queens, there are four queens in the deck one pursuit. So four queens and we're picking four of them times the choices for the last card. So there's 52 cards in a deck, which means that for the non queens, we have 48 to pick from, and we're choosing one since is just 48 then we want no face card, so we need to figure out the number of face cards so we know how many we can avoid. So for the face cards, we have the Jack, a queen and a king, and each of these therefore one pursuit because we have four jacks for queens and four cakes. So this means that we have 40 cards to pick from and we want all five to come from there. So our answers just 40. Choose five because we don't want any of the 12 face cards and plugging the send 40 choose five is 658,000 at eight Done. It wants exactly to face cards. So we have a number of ways to pick the face card times the number of ways to pick the non face cards. So we said over here that they're 12 total face cards. We want two of them times the remaining 40 cards where we're gonna pick three of them. And if we do this, we have 12. Choose to Times 40 choose three, which gives us an answer of 652,000 and a different ways that that scenario could play out. Then, For Part D, we have at least two face cards, so this is equal to the number with two plus the number with three plus the number with four. Close the number of five. So for the 1st 1 with two, we have 12 face cards picking too times 40 non face picking three plus 12 face cards picking three times 40 non face picking, too, plus 12 face cards aching four times 40 picking one plus 12 face cards. Picking five times 40 picking zero. And if we do this one, this requires a lot of computation, but we get 844,000 272 after we punch all those numbers in. And something to note with these types of problems is that notice that the top brackets add up to 52 all the time and the bottom bat brackets add up to five every time. And that's no coincidence. Then, for Part E, it says one heart, two diamonds in two clubs. So we have the number of ways to pick the heart, which there are 13 hearts because we have a 52 card deck divided equally amongst four suits. So have 13 pursuit. So a 13 choose one times 13 shoes to for the diamonds times 13 shoes to for the clubs. And if we do that, that's just 13 shoes too squared. Times 13 which gives us 79,092 and that's our final answer

Okay. This question asks us about a group of 20 flowers in which we're picking five of them to be in a flower show. So part A just wants the number of shows we could form from these flowers. And since it doesn't matter what order they're in because they're all going to be in the show, this is a combination. So we've got 20 flowers, totaled the pick from, and we're choosing five to be in the show. So 20 twos, five which simplifying. And our calculator just comes out to 15,504 different shows we could create, then part B. It asks us the same thing. Except now they're too special flowers that have to be included in the show of these 20. So you could do this entirely with combinations or without, But I'll show with So first we have to special flowers and we're picking two of them to be in the show times the remaining traces. So we have 18 non special flowers and we're picking three of them. So this is just 18. Choose three or 8 16 and you could leave out this first part because it is just equal to one

Four biographies, biographies and five mystery books. How many or how many different ways can one book of each type be selected? So we have five carry people to choose from? I mean, for biology books to choose from In five mystery books, we can multiply those together and we have 20 book variations, which is T.

For problems. Seven. We have a multiple choice test that has five questions. So five questions and each of those questions has four answers to that. We need to figure out how many ways can we fill out this test? And so how do we do this? Well, for a question one, we have four options and the same for question two. Sorry, I don't know why ratified? Same question to. And same for question 34 and five, all of which have four options. So we need to multiply four times itself five times, which comes out to 1000 and 24 ways that we can fill out this test and another way of writing. This is four race, the power of five. So if you've done exponents before, you will recognize that Ford of Power five is the same as four times for five times. So there's also equals 1024 ways. You can fill out this test


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