How to calculate the permutation & combination for this question?

shaique.uddin

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Hello all, I am an architect working on a problem related to permutation & combination and I am new to this forum. Kindly excuse my ignorance if I am approaching the forum incorrectly.

I am trying to figure out how to establish the method to calculate the permutation & combination for this question.
We have 6 A's, 6 B's, 6 C's, 6 D's & 6 E's Available to us. There are few conditions for selection though,
1. If A is picked, you must pick only 1 at a time.
2. If B is picked, you must pick 3 at a time.
3. If C is picked, you must pick 2 at a time.
4. If D is picked, you must pick 3 at a time.
5. If E is picked, you must pick 3 at a time.

Now based on these selection condition, We have to select 6 Objects from the collection.

What is the way to calculate the permutation & combination for the above problem.
Any guidance will be really appreciated.
Thank you.
Shaique.
 
Hello all, I am an architect working on a problem related to permutation & combination and I am new to this forum.
I am trying to figure out how to establish the method to calculate the permutation & combination for this question.
We have 6 A's, 6 B's, 6 C's, 6 D's & 6 E's Available to us. There are few conditions for selection though,
1. If A is picked, you must pick only 1 at a time.
2. If B is picked, you must pick 3 at a time.
3. If C is picked, you must pick 2 at a time.
4. If D is picked, you must pick 3 at a time.
5. If E is picked, you must pick 3 at a time.
I find this a vary confusing problem. Please explain more fully, with more examples.
 
Hello all, I am an architect working on a problem related to permutation & combination and I am new to this forum. Kindly excuse my ignorance if I am approaching the forum incorrectly.

I am trying to figure out how to establish the method to calculate the permutation & combination for this question.
We have 6 A's, 6 B's, 6 C's, 6 D's & 6 E's Available to us. There are few conditions for selection though,
1. If A is picked, you must pick only 1 at a time.
2. If B is picked, you must pick 3 at a time.
3. If C is picked, you must pick 2 at a time.
4. If D is picked, you must pick 3 at a time.
5. If E is picked, you must pick 3 at a time.

Now based on these selection condition, We have to select 6 Objects from the collection.

What is the way to calculate the permutation & combination for the above problem.
It will be helpful if you explain as much as possible in terms of your application rather than abstractly, and avoid technical terms you aren't sure of. For example, you ask for "permutation & combination", but that is two different things, and probably what you really want is neither! A permutation is a specific arrangement; a combination is a specific set; and we usually want only to count them, not to list them. I can't be sure what you want.

As I try to interpret it, you want the number of ways to make a set of 6 items, each of which can be one of the 5 types A, B, C, D, and E; items of a given type are not distinguished. Order doesn't matter, so ABBBCC is not considered a different choice than BCABBC; we can write all choices in alphabetical order for simplicity. But the number of B's must be a multiple of 3, and likewise D's and E's, while the number of C's must be even. So the following are examples of legal choices:

ABBBCC
BBBDDD
BBBEEE
DDDDDD
AACCCC

There may be few enough that listing them would be reasonably easy.

Please correct anything I have said wrong! And if you can tell us at least a little about what these things really are and why you have such rules, we will have a better idea what the rules really are, and whether there is a better way to accomplish your ultimate goal.
 
Hello all, I am an architect working on a problem related to permutation & combination and I am new to this forum. Kindly excuse my ignorance if I am approaching the forum incorrectly.

I am trying to figure out how to establish the method to calculate the permutation & combination for this question.
We have 6 A's, 6 B's, 6 C's, 6 D's & 6 E's Available to us. There are few conditions for selection though,
1. If A is picked, you must pick only 1 at a time.
2. If B is picked, you must pick 3 at a time.
3. If C is picked, you must pick 2 at a time.
4. If D is picked, you must pick 3 at a time.
5. If E is picked, you must pick 3 at a time.

Now based on these selection condition, We have to select 6 Objects from the collection.

What is the way to calculate the permutation & combination for the above problem.
Any guidance will be really appreciated.
Thank you.
Shaique.
We have 6 A's, 6 B's, 6 C's, 6 D's & 6 E's Available to us. This is clear to me.

1. If A is picked, you must pick only 1 at a time.
2. If B is picked, you must pick 3 at a time.
3. If C is picked, you must pick 2 at a time.
4. If D is picked, you must pick 3 at a time.
5. If E is picked, you must pick 3 at a time.

The above says to me that 1st you pick one of the 30 letters. Do you put it back before picking again? You ultimately want to choose 6 letters/objects. If C is picked, you must pick 2 at a time. So far you picked C and two other letters. Then you pick another? If it is then you can't pick exactly 6!
 
Hi Everyone, I apologize for not being able to describe properly. The question revolves around filling up a grid of Points with those A,B,C,D. Something like this:
1610988595024.png

Here is another example where the Grid size increases. In this case the count of A, B, C & D also increases to fill in the Grid.

1610989169441.png

I thought, if I could figure out the number of possibilities for one row , I could apply the same logic for the rest and would have a solution to work upon.
@Dr.Peterson yes, the way you have shown the legal choices is what I am trying to get to. The Order does Matter, so CCABBB , BBBACC & BBBCCA are three different choices.
@Jomo Once we pick a letter, we don't put it back.
I hope this explains the question better than before. Please let me know if there is still any doubts.
Thank you once again everyone.
Best,
Shaique
 
I'm not sure you've stated the entire problem yet; please give all the rules now that we know about the grid. (Is the idea that there will be a row for each possibility? When you expand the grid, will there still be enough of each letter to fill a whole row if needed?)

In particular, it appears that in any row, all of each letter except for A must be consecutive, which I don't think you've explicitly stated. Maybe your "n at a time" means "n consecutive", not just "a multiple of n" as I suggested. (It isn't clear to me.)

You also haven't shown your attempt to solve the problem, which we expect to see:
 
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