Math Experts

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cincyhorn

100+ Posts
My daughter is in the fourth grade. Up until now helping with her homework has been cake. I don't pretend to be a math genius by any stretch, by thought I was smarter than a fourth grader.

She came home with following problem. At first, it seemed like simply multiplication, now I'm not so sure. It seems like I remember something like this in my high school stat class. Here's the question, please help me with the steps to get the answer.

John is goes to the sandwich shop for lunch. The shop has six types of meats, four kinds of cheeses and ten different condiments, how many sandwich combinations does he have to choose from?

Thanks!
 
Sounds like you just multiply the number of each item together. Here's a link to a prob that looks very similar.

Link
 
If you have to have one of each (no more, no less) then it is simply multiplication. 6x4x10=240 sandwich combinations.

If you are able to select multiple within a kind, and/or none within a kind (cheddar & provolone w/ no condiments) then it gets trickier. For the meats there would be 1 combination which had 6 meats, 6 combinations with 5 meats, 15 combinations with 4 meats, 20 combinations with 3 meats, 15 combinations with 2 meats, 6 options with 1 meat and 1 option with no meats, for a total of 64 meat options... which you would then multiply by the cheese options and then by the condiment options, for a much higher number.

I guess if you were not limited by the number of times you could select a single item (double/triple cheddar), then it gets even bigger... that said, I think they were likely looking for the first solution.
 
This does not sound like a 4th grade math problem, unless you're leaving out some assumptions. If you have exactly one meat, one cheese, and one condiment on a sandwich, the total number of combinations is:

6 x 4 x 10 = 240

But of course at Subway you can get as many condiments as you want (or no condiments at all), so if this is a real life problem, the answer is:

2^(6 + 4 + 10) - 1 = 1,048,575 combinations

You're subtracting 1 for the case of a sandwich with no meat, no cheese, and no condiments - which is not really a sandwich. Man shall not live by bread alone!
 
i feel like 99% of kids are smarter than me when i was that age.

My 3 year old says things that just astound me and i think no way was i saying things like that at his age.
 
AstroVol, check my math, but one of us is wrong and I fear it is me. If you can have 1 or 0 of any specific item (I can have a sandwich with 6 meats or 0 meat, or any combination between) then there are 64 combos of meat, 16 combos of cheese and 1024 combos of condiments, multiplied together that's 884,736 potential combinations of the 20 potential ingredients (including many all condiment sandwichs as well as a dry bread "sandwich").

What am I doing wrong?
 
mia, I think you did a typo while entering your numbers into the calculator and entered '54' instead of '64' for the meats
 
Thanks everyone! I orginally landed on 240, assuming 1,1,1, but knew if there were many more combinations. I didn't leave out any assumptions, although it is possible the teacher provided asumptions verbally.
 
I think the correct answer is 240 when you are in the fourth grade, but the 1 million some odd when you are in the ninth grade.
 
4th grade teacher here; that problem is way too hard for fourth grade. On the TAKS test we have seen pictures of the two different things to make combinations of; never have seen three. iow, maybe condiments and meat, four kinds of condiments, and three kinds of meat.

I don't know why they would make it so much harder by throwing three things in there. Maybe the teacher or kids are bored?
 
Sounds like an easy way to see if the parents are doing the homework.
wink.gif
 
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