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Loki123

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You have 5 white flowers and 4 red. In how many ways can you make a flower arrangement if three flowers have to be white. My idea was to see in how many ways I can arrange three white flowers and multiply it by how many ways I can get out of the rest, 6 flowers, for two places. I got 150, the answer is 81.IMG_20220406_082036.jpg
 
Loki123 said:
You have 5 white flowers and 4 red. In how many ways can you make a flower arrangement if three flowers have to be white. My idea was to see in how many ways I can arrange three white flowers and multiply it by how many ways I can get out of the rest, 6 flowers, for two places. I got 150, the answer is 81.View attachment 32013
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In the arrangement:

Does the TOTAL number of flowers HAVE to be 9?

The # of white flowers is EXACTLY 3, or AT LEAST 3?
 
My idea was to see in how many ways I can arrange three white flowers and multiply it by how many ways I can get out of the rest, 6 flowers, for two places.
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Why do you say "for 2 places"? This seems to imply that an arrangement must have 5 flowers ???

Can you please state the question EXACTLY as it was given to you?
 
Subhotosh Khan said:
In the arrangement:

Does the TOTAL number of flowers HAVE to be 9?

The # of white flowers is EXACTLY 3, or AT LEAST 3?
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So you have 9 flowers
The flower arrangement needs to be made out of 5
Out of those 5, 3 have to be white
 
Please give the exact and complete wording of the problem as it was given to you.

Often the reason that a student has difficulty with a problem is that the student has misinterpreted the wording of the problem. That means the student’s paraphrase is worse than useless.

Giving the exact problem is one of our guidelines. Please follow it.
 
JeffM said:
Please give the exact and complete wording of the problem as it was given to you.

Often the reason that a student has difficulty with a problem is that the student has misinterpreted the wording of the problem. That means the student’s paraphrase is worse than useless.

Giving the exact problem is one of our guidelines. Please follow it.
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You have 5 white flowers and 4 red flowers. In how many ways can you make a flower arrangement if at least three flowers in it have to be white?
 
Subhotosh Khan said:
Are those white flowers distinguishable - like one white rose, one white gardenia, etc. ?



Are those white flowers distinguishable - like one red rose, one red carnation, etc. ?
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Doesn't say, and that's why I have problems. I don't know whether it's combinations without repetition, with repetition, variation with or without repetition. I was thinking we could see for what we get 81 as the answer and then figure that out.
 
Loki123 said:
You have 5 white flowers and 4 red flowers. In how many ways can you make a flower arrangement if at least three flowers in it have to be white?
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That was not in your original question, and clarifies one issue. The other big issue is, how many flowers are to be in the arrangement? It would appear that it can be any number (up to 9). Taking it this way, I get 256, assuming the flowers are distinguishable.

If they are not, then you have either 3, 4, or 5 white flowers, and either 0, 1, 2, 3, or 4 red, giving 3*5=15 ways.

Loki123 said:
Doesn't say, and that's why I have problems. I don't know whether it's combinations without repetition, with repetition, variation with or without repetition. I was thinking we could see for what we get 81 as the answer and then figure that out.
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You're saying that this comes from a book, which gives the answer as 81? (And not that somebody you can't trust gave that answer?)

On the whole, it's just a very poorly worded problem, or else their answer is wrong, or both. Can you just skip it?
 
Dr.Peterson said:
That was not in your original question, and clarifies one issue. The other big issue is, how many flowers are to be in the arrangement? It would appear that it can be any number (up to 9). Taking it this way, I get 256, assuming the flowers are distinguishable.

If they are not, then you have either 3, 4, or 5 white flowers, and either 0, 1, 2, 3, or 4 red, giving 3*5=15 ways.


You're saying that this comes from a book, which gives the answer as 81? (And not that somebody you can't trust gave that answer?)

On the whole, it's just a very poorly worded problem, or else their answer is wrong, or both. Can you just skip it?
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I just compared notes, it is supposed to say flower arrangement out of 5 flowers. Does this make it work?
 
5 flowers, at least 3 white.

If 3 are white, then we have 10 possible placements for the two red flowers

If 4 are white, then we have 5 possible placements for the red flower.

If five are white, then there is no possible place for a red flower.

That gets me to 16 possible distinguishable arrangements if the flowers of the same color are otherwise indistinguishable.
 
JeffM said:
5 flowers, at least 3 white.

If 3 are white, then we have 10 possible placements for the two red flowers

If 4 are white, then we have 5 possible placements for the red flower.

If five are white, then there is no possible place for a red flower.

That gets me to 16 possible distinguishable arrangements if the flowers of the same color are otherwise indistinguishable.
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Isn't that when they are not distinguishable? If 4 are white and we mix those up we'll have more possibilities. Also if we pick differnt three white flowers
 
Loki123 said:
I just compared notes, it is supposed to say flower arrangement out of 5 flowers. Does this make it work?
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Why did you claim to quote the entire problem and leave this out???
Loki123 said:
Also why do i get 60 with the same method? Please help
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You haven't shown any work that yielded 60, so we can't tell what you did wrong. Clearly you didn't really use the same method.

Here is what pka did:

If there are 3 white and 2 red, there are 5C3 * 4C2 ways = 60.​
If there are 4 white and 1 red, there are 5C4 * 4C1 ways = 20.​
If there are 5 white and 0 red, there are 5C5 * 4C0 ways = 1.​
The sum is 81.​

I suspect you did only the first case.
 
pka's answer assumes that all flowers ARE distinguishable (no two flowers are the same even if their colour matches)
It also assumes that the ordering of flowers within each arrangement doesn't matter

IMO it's a bad question since it didn't specify either of these things. The puzzle here is to work out what the question is, given that the desired answer is 81.
 
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