Total Number of Possible Combinations

In summary, the conversation revolves around a graphic designer seeking help with adding a "total number of possible combinations" to a menu for a hotdog restaurant. There are 10 types of sausage and 65 different toppings, leading to a total of 275 combinations. The discussion also includes a clarification on whether all toppings and sausages can be ordered together, leading to a formula of 2 to the 66th power for all possible combinations. It is then clarified that there are 265 different combinations of toppings alone, and 10 * 265 combinations of toppings and sausages together. The conversation ends with a final formula of 11 * 265 for all possible hotdog combinations.
  • #1
tostenson
3
0
Hello, I am a graphic designer working on a menu for a friend of mine and math was never my strong suit. Also, add the fact that I've been out of school for some time and don't do math regularly. Anyway, I have a pretty simple question that I could use some help with if someone doesn't mind.

I'm wanting to add a "total number of possible combinations" to his menu, since he has quite a few options.

So here's my query:

He has 10 types of meat
He has 65 different types of toppings

How many different combinations can he make out of all these items?

Thanks in advance for the help :)
 
Mathematics news on Phys.org
  • #2
Can you narrow the problem down some? Would it be possible to order a pizza (I assume that's what you're talking about) with all 10 types of meat and all 65 types of toppings? Or are there limits on the numbers of types of meat and toppings?
 
  • #3
If you are wanting to brag about the large number of possible topping choices available, you answer is 275 = 37778931862957161709568. This allows the choices of "everything" or nothing and everything in between.
 
  • #4
Sure to help narrow it down, he has a hotdog restaurant, which has 10 types of sausage choices and 65 different toppings. Though, I think LCKurtz nailed my question. The point was to say "you can choose from ___ different flavor combinations". Thanks :)
 
  • #5
tostenson said:
Sure to help narrow it down, he has a hotdog restaurant, which has 10 types of sausage choices and 65 different toppings. Though, I think LCKurtz nailed my question. The point was to say "you can choose from ___ different flavor combinations". Thanks :)
But I'm guessing that you can't order a hot dog with, say, four hot dogs on it, so you won't get all of the combinations that LCKurtz listed.
 
  • #6
You're right Mark. So the formula would be 2 to the 66th power then?
 
  • #7
tostenson said:
You're right Mark. So the formula would be 2 to the 66th power then?

I think so.
 
  • #8
tostenson said:
You're right Mark. So the formula would be 2 to the 66th power then?

Dr. Seafood said:
I think so.

I don't think so. Let's work with the toppings first. Since there are 65 of them, and anyone of them could be included, there are 265 different combinations of the toppings. In case that's not clear, let's suppose there is just one topping, and it is either put on or not. That's two combinations for the one topping, which happens to be 21.

Now let's suppose there are two toppings, A and B. The different combinations are:

(no topping)
A
B
A and B

That makes four combinations for the two toppings, which happens to be 22.

In general, if there are n toppings, there will be 2n combinations of the toppings. For the 65 toppings, this means there are 265 possible combinations. This runs the gamut from no toppings at all, all the way to all 65 of them being on the hot dog, as well as every intermediate possibility.

OK, now let's figure out the combinations with a sausage included. Since there are 10 different sausages, and we are assuming that a hot dog won't have more than one sausage, for each choice of sausage there are 265 ways we can top it. That makes 10 * 265 different hot dog combinations.

If we also include the possibility that some doesn't want the sausage included, that makes 11 * 265 different combinations, one of which would be a hot dog with no sausage, and no toppings. IOW, just a bun.
 

What is "Total Number of Possible Combinations"?

The total number of possible combinations refers to the number of unique ways in which a set of items can be arranged or selected. It is commonly used in mathematics, statistics, and computer science.

How is the total number of possible combinations calculated?

The total number of possible combinations can be calculated using the formula nCr = n! / (r!(n-r)!), where n represents the total number of items and r represents the number of items being selected.

What is the difference between combinations and permutations?

Combinations refer to the different ways in which a set of items can be selected without considering the order in which they are selected. Permutations, on the other hand, take into account the order of the selected items.

Why is the total number of possible combinations important?

The total number of possible combinations is important because it helps to determine the probability of a specific outcome. It is also used in various fields such as cryptography, genetics, and economics.

What are some real-life examples of total number of possible combinations?

The total number of possible combinations can be seen in various real-life scenarios, such as choosing a combination for a lock, selecting a lottery ticket, or arranging a deck of cards. It is also used in creating unique passwords, designing experiments, and analyzing data in genetics.

Similar threads

  • General Math
Replies
1
Views
685
Replies
1
Views
2K
Replies
14
Views
2K
  • General Math
Replies
3
Views
2K
  • Precalculus Mathematics Homework Help
Replies
6
Views
597
  • General Math
Replies
4
Views
4K
Replies
4
Views
1K
  • General Math
Replies
4
Views
4K
  • General Math
Replies
2
Views
840
Back
Top