Too much information? Or, what kind of formula to use?

[jazz]

Jack went out for a 4-course meal where he had a choice of 3 salads, 3 appetizers, 4 entrees and 5 deserts. How many 4-course meals are possible?

I came up with 4.
1) Entree, appetizer, salad, desert
2) Entree, appetizer, salad, desert
3) Entree, appetizer, salad, desert
4) Entree, desert, desert

That just seemed too easy. Would someone tell me if it is correct?

If I did that correct then I have another one that might be similar but it might need a formula, I don't know.

Jack's combination lock requires three numbers to open. Each number in the combination is an integer between 0 and 9 (inclusive). How many different combinations are possible?

I came up with 27 and I got that by multiplying 3 times 9 is that correct?

These word problems for core standards are getting really strange. :???:

 

[srmichael]

Jack went out for a 4-course meal where he had a choice of 3 salads, 3 appetizers, 4 entrees and 5 deserts. How many 4-course meals are possible?

I came up with 4.
1) Entree, appetizer, salad, desert
2) Entree, appetizer, salad, desert
3) Entree, appetizer, salad, desert
4) Entree, desert, desert

That just seemed too easy. Would someone tell me if it is correct?

If I did that correct then I have another one that might be similar but it might need a formula, I don't know.

Jack's combination lock requires three numbers to open. Each number in the combination is an integer between 0 and 9 (inclusive). How many different combinations are possible?

I came up with 27 and I got that by multiplying 3 times 9 is that correct?

These word problems for core standards are getting really strange. :???:

For you first question, I assume that he is to choose only one item from each course (i.e. he won't pig out on 2 desserts ). With that assumption, if you have x items in one group and y items in another group and z items in another group and so on for as many groups that you have, the total number of ways you can choose one item from each is the product of the number of each items in each group. In my example it would be (x)(y)(z).

So using your information, how many 4-course meals are possible?

P.S. If my assumption is not correct, then that changes the problem entirely and we can reconvene if that is the case.

 

[HallsofIvy]

In what you list,
1) Entree, appetizer, salad, desert
2) Entree, appetizer, salad, desert
3) Entree, appetizer, salad, desert
4) Entree, desert, desert

The first three look exactly the same- and the fourth is not a "4 course meal". I think you are completely misunderstanding the problem. First, a "four course meal" necessarily consists of "Entree, appetizer, salad, desert". You get different meals by using different appetizers, different salads, etc.

You are told that there are "a choice of 3 salads" so even if he chose exactly the same entree, appetizer, and desert, you could have three different meals just with different salads. For example, suppose the appetizers were "calamari", "clams casino", and "antipasto", the salads were "Caesar salad", "macaroni salad", and "green salad", the entrees were "swordfish steak", "t-bone steak", "grilled chicken", and "fried chicken", and the deserts were "apple pie", "layer cake", "lemon meringue pie", fruit compote, and brownies.

Then one meal would be "calamari, Caesar salad, swordfish steak, apple pie". Another would be "calamari, Caesar salad, t-bone steak, apple pie". A third would be "calamari, Caesar salad, grilled chicken, apple pie" and a fourth would be "calamari, Caesar salad, fried chicken, apple pie". That's four where I have changed only the entree. Think how many more there would be changing the appetizers, the salads, etc.

What you need here is the "fundamental principle of counting". Does your textbook have that?

 

[jazz]

I think inside the box instead of expanding my thoughts

Thanks for helping me to think outside the box. Also, no my book doesn't have Fundamentals of Counting which would probably help with both of my questions. Is it easiest to simply write out the numbers like what was recommended by another person in the forum or is there another way to make this less confusing? And thanks again.

In what you list,
1) Entree, appetizer, salad, desert
2) Entree, appetizer, salad, desert
3) Entree, appetizer, salad, desert
4) Entree, desert, desert

The first three look exactly the same- and the fourth is not a "4 course meal". I think you are completely misunderstanding the problem. First, a "four course meal" necessarily consists of "Entree, appetizer, salad, desert". You get different meals by using different appetizers, different salads, etc.

You are told that there are "a choice of 3 salads" so even if he chose exactly the same entree, appetizer, and desert, you could have three different meals just with different salads. For example, suppose the appetizers were "calamari", "clams casino", and "antipasto", the salads were "Caesar salad", "macaroni salad", and "green salad", the entrees were "swordfish steak", "t-bone steak", "grilled chicken", and "fried chicken", and the deserts were "apple pie", "layer cake", "lemon meringue pie", fruit compote, and brownies.

Then one meal would be "calamari, Caesar salad, swordfish steak, apple pie". Another would be "calamari, Caesar salad, t-bone steak, apple pie". A third would be "calamari, Caesar salad, grilled chicken, apple pie" and a fourth would be "calamari, Caesar salad, fried chicken, apple pie". That's four where I have changed only the entree. Think how many more there would be changing the appetizers, the salads, etc.

What you need here is the "fundamental principle of counting". Does your textbook have that?

 

[wjm11]

Thanks for helping me to think outside the box. Also, no my book doesn't have Fundamentals of Counting which would probably help with both of my questions. Is it easiest to simply write out the numbers like what was recommended by another person in the forum or is there another way to make this less confusing? And thanks again.

You would find it very tedious and time consuming to write out all the possibilities. Instead, Google "fundamental principle of counting" and review the various sites, such as:

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut55_count.htm

which will provide some easy and insightful examples.