$Extreme equation problem$

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Extreme equation help So my work is offering $6,000 to anyone who can solve this.

https://www.instagram.com/p/Cc1cbJgp3h2/igshid=YmMyMTA2M2Y

I?m no good at math and I?m hoping someone bored on here could help me out. Here is a link to the menu.

https://rudyssteakhouse.com/dinner

these are the numbers:

9 salad option 3 soup options 26 entrees (13 require temp) 2 veggies 5 starch 18 add ons 6 meat temps

Equations

Kyle Hooper

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Mathe

Both links are broken
Nirenberg

I can view either of the links too.
Mathe

You mean you can't*
Nirenberg

Oh sorry, I can NOT.
Mathe

I found the links. The thing is, there are some level of assumptions that have to be made on this. Since the contest ends this weekend, you could wait to see the results of the contest and not Accept our answer if you did not win the prize. It's tricky to answer then.
Nirenberg

It works if you copy past the following link in your browser: https://www.instagram.com/p/Cc1cbJgp3h2/?igshid=YmMyMTA2M2Y
Daniel90

There is not enough information given about the possible choices, and one needs to go through the menu for such information to compute what you are asking which is very time consuming for the offered bounty here.
Aman R

Links are broken! Kindly attach image via latex coding
Kyle Hooper

9 salad option 3 soup options 26 entrees (13 require temp) 2 veggies 5 starch 18 add ons 6 meat temps

Mathe

I found the links. The thing is, there are some level of assumptions that have to be made on this. Since the contest ends this weekend, you could wait to see the results of the contest and not Accept our answer if you did not win the prize. It's tricky to answer then.
Nirenberg

It works if you copy past the following link in your browser: https://www.instagram.com/p/Cc1cbJgp3h2/?igshid=YmMyMTA2M2Y
Daniel90

There is not enough information given about the possible choices, and one needs to go through the menu for such information to compute what you are asking which is very time consuming for the offered bounty here.
Aman R

Links are broken! Kindly attach image via latex coding
Kyle Hooper

9 salad option 3 soup options 26 entrees (13 require temp) 2 veggies 5 starch 18 add ons 6 meat temps

Answer 1

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Let?s count the number of each item on the menu separately.

- Number of Entrée Selections: There are 13 entrees that require mean temperature selection and 13 others that do not require mean temperature selection. There are also two veggies. So the number of different entrée selections is \[ 13+13\times 6+2=93. \]
- Number of Starter Selection

Starters could be soup or salad and we have a total number of \[9+3=12\] options.

- Number of Starch is \[5\]

- Number of add ons

There are 18 add ons and we would like to choose 2. It is simply the number of ways one can choose 2 objects from 18 objects (assuming that one does not choose two of the same add ons) is \[{18 \choose 2}=\frac{18!}{(18-2)!\times 2!}=\frac{18\times 17}{2}=9\times 17=153.\]

Therefore the total number different combinations of meals that can be created from Rudy's Steakhouse dinner menu is \[93\times 12 \times 5 \times 153=853740.\] Indeed if one orders a different combination every day it will take about \[\frac{853740}{365}=2339.01 \text{years}\] to try all possible combinations at Rudy's Steakhouse!

Nirenberg

$Extreme equation problem$

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