Total Options: bags of coal, logs, kindling, and firelighters

Margip

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Nov 27, 2015
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Hi

I'm sure there must be an easy way to work this out.

I have four products - coal, logs, kindling and firelighters. Product 1 has 8 possible purchasing options (numbers of bags - 1, 2, 3, 4, 5, 10, 15, 20), Product 2 has the same 8 options, as does product 3 and product 4 has 5 options. So i have 29 possible single orders (8 + 8 + 8 + 5)

A customer can order any one of the options of the four products.

At one end of the scale they can order just 1 product, up to an option on each of the 4 products.

The different options on each product are numbers of bags, so they would only ever order one option of any of the four products. They may want coal and firelighters in any quantity, or logs and kindling, or logs, kindling, coal and firelighters.

How can i work out how many total possible combinations there are?

Any help would be much appreciated.
 
I have four products - coal, logs, kindling and firelighters. Product 1 has 8 possible purchasing options (numbers of bags - 1, 2, 3, 4, 5, 10, 15, 20), Product 2 has the same 8 options, as does product 3 and product 4 has 5 options. So i have 29 possible single orders (8 + 8 + 8 + 5)

A customer can order any one of the options of the four products.

At one end of the scale they can order just 1 product, up to an option on each of the 4 products.
If I'm understanding this correctly, the appropriate technique would probably be an application of the "Counting" or "Multiplication" Principle. (here, here, or here)

So think of there being four boxes, each of which can accept of the listed types of outcomes. This means, for instance, that the first box (for coal) can accept any of nine options: no bags, a one-pound bag, a two-pound bag, etc, up to a twenty-pound bag.

Count the numbers of options for each box, and then apply the Principle. ;)
 
If I'm understanding this correctly, the appropriate technique would probably be an application of the "Counting" or "Multiplication" Principle. (here, here, or here)

So think of there being four boxes, each of which can accept of the listed types of outcomes. This means, for instance, that the first box (for coal) can accept any of nine options: no bags, a one-pound bag, a two-pound bag, etc, up to a twenty-pound bag.

Count the numbers of options for each box, and then apply the Principle. ;)

BTW, this method of counting counts a 'no order' as an order [zero of each quantity] so if you must order something for it to count as an order, just subtract one from that total.
 
I'm sure there must be an easy way to work this out.
I have four products - coal, logs, kindling and firelighters. Product 1 has 8 possible purchasing options (numbers of bags - 1, 2, 3, 4, 5, 10, 15, 20), Product 2 has the same 8 options, as does product 3 and product 4 has 5 options. So i have 29 possible single orders (8 + 8 + 8 + 5). A customer can order any one of the options of the four products.
I have read all the replies. I agree! But still I hope you will play the back-of-the-book game with us.

You look up the answer: \(\displaystyle 9^3\cdot 6\) or maybe \(\displaystyle (9^3\cdot 6)-1\).
Now it is your job to explain the answer.
 
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