Combinations and Permutations

Question

I understand that most combination word problems use words such as “and” (which means to multiply) and some use the word “or” (which means to add).

However, are there any instances where a combination or permutations math question can include both “and” and “or”? If so, how do you go about solving those kinds of problems?

For instance, with combo #1 you can get sides A and B, with combo #2 you can get sides C and D, with combo #3 you can get sides E and F. All combos come with a beverage choice of water, milk, or lemonade. How many combinations can be made?

Answer 1

Sage,

There is a general rule in counting called the multiplication rule

In this problem there are 2 side choices for combo#1, 2 for #2, 2 for #3 and 3 for drinks so there are 2*2*2*3=24 different combinations of combo's and drinks.

Hope this helps

Jim

Answer 2

The way the information is posed, it appears that Combos 1, 2 and 3 are fixed with respect to their sides. That is, Combo 1 can never have C, D, E, or F as sides, Combo 2 can never have A, B, E, or F as sides and Combo 3 can never have A, B, C, or D as sides.

The only variable option is the drink. There are 3 choices for drink for each of the 3 Combos, making the total number od food+drink combinations = 3 combos x 3 drinks = 9.