Arrangement of items after removing some of the items

  • Thread starter desmond iking
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In summary: What am I missing?In summary, the conversation revolves around determining the possible number of arrangements of 5 randomly chosen cubic blocks from a bag containing 4 red blocks and 3 yellow blocks. The participant suggests using the formula 7P5/(4! X 3!) to calculate the answer, but others point out that the answer cannot be fractional. More information is needed to accurately solve the problem.
  • #1
desmond iking
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Homework Statement


A bag contains 4 red cubic blocks, 3 yellow cubic blocks, . Five cubic blocks are removed randomly from the bag and arranged in line . How many arrangements are possible?

the ans is 8 .

my working is 7P5/(4! X 3!) =17.5 .

my ans is rather weird.


Homework Equations





The Attempt at a Solution

 
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  • #2
Are we to assume that blocks of the same color are indistinguishable?
 
  • #3
desmond iking said:

Homework Statement


A bag contains 4 red cubic blocks, 3 yellow cubic blocks, . Five cubic blocks are removed randomly from the bag and arranged in line . How many arrangements are possible?

the ans is 8 .

my working is 7P5/(4! X 3!) =17.5 .

my ans is rather weird.


Homework Equations





The Attempt at a Solution


The number of arrangements cannot possibly be 17.5; it cannot be fractional.

Instead of just writing down some formulas, you need to explain the logic, so that we are in a position to assist you. If your thinking is "off", we need to know first what it is before we can put you on the right track.
 
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  • #4
Ray Vickson said:
The number of arrangements cannot possibly be 17.5; it cannot be fractional.

Instead of just writing down some formulas, you need to explain the logic, so that we are in a position to assist you. If your thinking is "off", we need to know first what it is before we can put you on the right track.

my reasoning is first i choose 5 blocks from the 7 blocks. then since there 're 4 same colour red and 5 same colour yellow, so i divide it by 4! X 3!
 
  • #5
You need to provide more information. Is that really the full problem statement? I don't see an interpretation that yields the answer 8. For example, if you end up choosing 4 red and 1 yellow, I'd say that 5 arrangements are possible, and if you end up choosing 3 red and 2 yellow, I'd say that 10 arrangements are possible.
 

1. How does removing items affect the arrangement of remaining items?

Removing items can cause the remaining items to be rearranged in a different order, depending on the method of removal and the initial arrangement. For example, if items are removed in a random order from a shelf of books, the remaining books may be shifted around to fill in the gaps.

2. Can removing items change the overall organization or structure of a group of items?

Yes, removing items can change the organization or structure of a group of items, especially if the removed items were holding other items in place. For instance, removing a supporting item from a stack of books can cause the remaining books to collapse or shift.

3. What factors can influence the arrangement of items after removal?

The arrangement of items after removal can be influenced by various factors, such as the initial organization of the items, the method of removal, and the size and weight of the items. Other factors may include external forces, like gravity or air flow, that can shift the remaining items.

4. Is there a way to predict the arrangement of items after removing some of them?

In some cases, it may be possible to predict the arrangement of items after removing some of them, especially if the initial arrangement and method of removal are known. However, due to the potential influence of various factors, it may not always be possible to accurately predict the final arrangement.

5. How can the arrangement of items after removal be controlled or manipulated?

The arrangement of items after removal can be controlled or manipulated by carefully planning the initial arrangement and method of removal. Additionally, using supports or dividers can help maintain a desired arrangement even after removing some items. In some cases, external forces, such as magnets or air flow, can also be used to manipulate the arrangement of items.

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