#### Kashmirnutshell

##### New member

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A. .4 B. .04 C. .1 D .01

- Thread starter Kashmirnutshell
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A. .4 B. .04 C. .1 D .01

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Suppose you are going to place the 4 drinks in a line, and you have the spots for them in front of you. You are going to put one of the drinks in the first spot. How many drinks do you have from which to choose?

How about for the second spot, and so on?

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3 and then 2 and then 1

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Call the sodas A, B, C and D. How many ways can you write down just those four letters. I will start you off

ABCD

ABDC

ACBD

ABDC

keep going....

Now once you figure out all the possibly outcomes, then you need to figure out how many of those outcomes will be correct.

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Yes your right there is an approx sign in front of the choices. Im stuck on the method you use to determine how many possibilities there areIn my opinion NONE of those choices are correct.

In how many different ways can participant guess all 4 correctly and how many different ways can a participant rank the 4 sodas

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Yes, 4 choices for the first spot, 3 for the second, 2 for the third, and 1 for the fourth. Using the fundamental counting principle, then how many ways can you order the 4 drinks?3 and then 2 and then 1

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ADBCCall the sodas A, B, C and D. How many ways can you write down just those four letters. I will start you off

ABCD

ABDC

ACBD

ABDC

keep going....

ACDB

ADCB

BACD

BCAD

BDAC

BDCA

BCDA

Seems like this can go forever. There isnt a method to determine that with out writing all that out? Guys like me have to write all that but you guys can do this stuff in your head

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10?Yes, 4 choices for the first spot, 3 for the second, 2 for the third, and 1 for the fourth. Using the fundamental counting principle, then how many ways can you order the 4 drinks?

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You don't want to add, you want to multiply...

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Lol thank you for your help. As You can see, i need it. 24?You don't want to add, you want to multiply...

Well, in your previous brute force attempt, you listed more than 10 possibilities, so we know for sure that can't be the answer. This suggests that simply adding the number of possibilities is not correct. But let's investigate why that might be, and see if we can't stumble upon what *is* the correct answer. Suppose for a moment there were only two slots and we could choose __from__ four sodas for the first slot and __choose from__ three for the second slot. Right away we can begin listing the possibilities for the first slot (again, labeling the sodas A, B, C, and D):

__of the three other sodas__. We know that the second slot has three possibilities, so we can fill in the missing information:

**for each of** the four sodas we __can__ put in the first slot, we have three choices for the second slot. The words I've bolded are the very important bit, as thinking about what those words mean with reference to word problems should give you an inclination as to why it makes intuitive sense to multiply rather than add.

**Edit:** To appease the grammar gods, I've inserted a few words to make my meaning extremely explicit. These inserted words are underlined.

- A[?]
- B[?]
- C[?]
- D[?]

- A[?]
- AB
- AC
- AD

- B[?]
- BA
- BC
- BD

- C[?]
- CA
- CB
- CD

- D[?]
- DA
- DB
- DC

Last edited:

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Yes!, Guys like you have to write all that but we guys can do this stuff in your head. The way we learned the short cuts was by seeing what these lists look like and then try to figure out shortcut.ADBC

ACDB

ADCB

BACD

BCAD

BDAC

BDCA

BCDA

Seems like this can go forever. There isnt a method to determine that with out writing all that out? Guys like me have to write all that but you guys can do this stuff in your head

The list will not go on forever. Now please complete the list

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No, you are NOT putting four sodas in the first slot. You are putting ONE SODA from a possible four into the 1st slot.Well, in your previous brute force attempt, you listed more than 10 possibilities, so we know for sure that can't be the answer. This suggests that simply adding the number of possibilities is not correct. But let's investigate why that might be, and see if we can't stumble upon whatisthe correct answer. Suppose for a moment there were only two slots and we could choose four sodas for the first slot and three for the second slot. Right away we can begin listing the possibilities for the first slot (again, labeling the sodas A, B, C, and D):

Here [?] denotes a "wildcard" - that particular slot can be anything. We know that the second slot has three possibilities, so we can fill in the missing information:

- A[?]
- B[?]
- C[?]
- D[?]

In other words,

- A[?]

- AB
- AC
- AD
- B[?]

- BA
- BC
- BD
- C[?]

- CA
- CB
- CD
- D[?]

- DA
- DB
- DC
for each ofthe four sodas we put in the first slot, we have three choices for the second slot. The words I've bolded are the very important bit, as thinking about what those words mean with reference to word problems should give you an inclination as to why it makes intuitive sense to multiply rather than add.

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Yes, there are \(4!=24\) different ways to order the drinks. In general, there are \(n!\) ways to order \(n\) objects. So, can you now answer the question?Lol thank you for your help. As You can see, i need it. 24?

Fine. If it will make you happy, I'll insert some words to "fix" my minor grammatical errors that anyone with any bit of proficiency in English would gloss over because my meaning is fairly clear.No, you are NOT putting four sodas in the first slot. You are putting ONE SODA from a possible four into the 1st slot.

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Yes, there are \(4!=24\) different ways to order the drinks. In general, there are \(n!\) ways to order \(n\) objects. So, can you now answer the question?

96? 4 sodas w 24 possible spots? 24×4?