Joy plans to visit a sub shop for a sandwich. At the shop, she can pick from a roll (R), bread (B), or wrap (W). For meats, there's ham (H) and turkey (T), along with two cheese options: Swiss (S) and American (A). Joy wants a list of her options before she goes. Assuming she selects one choice from each category, what combinations make up her list?A. RBW, RBH, RBT, RBS, RBA B. RSA, BSA, RHT, BHT, HSA C. RH, RT, BH, BT, WH D. RHS, RHA, RTS, RTA, BHS, BHA, BTS, BTA, WHS, WHA, WTS, WTA

Mathematics · Middle School · Thu Feb 04 2021

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The correct list of all possible sandwich combinations that Joy could make, given that she selects one choice from each category (bread type, meat, and cheese), is:

D. RHS, RHA, RTS, RTA, BHS, BHA, BTS, BTA, WHS, WHA, WTS, WTA

Here's the breakdown of how we reach this conclusion:

First, we have 3 options for the type of bread or wrapper: roll (R), bread (B), or wrap (W).

Then, there are 2 options for the type of meat: ham (H) and turkey (T).

Finally, we have 2 options for cheese: Swiss (S) and American (A).

Now, for each bread type, Joy can have either ham or turkey, and with each meat choice, she can have either Swiss or American cheese. So, for each bread type, there are 2 meat options multiplied by 2 cheese options, which gives us 4 different combinations per bread type. We have 3 bread types, so in total, we have 3 x 4 = 12 different sandwich combinations.

Here they are:

For roll (R), she can have: 1. Ham and Swiss (RHS) 2. Ham and American (RHA) 3. Turkey and Swiss (RTS) 4. Turkey and American (RTA)

For bread (B), she can have: 5. Ham and Swiss (BHS) 6. Ham and American (BHA) 7. Turkey and Swiss (BTS) 8. Turkey and American (BTA)

For wrap (W), she can have: 9. Ham and Swiss (WHS) 10. Ham and American (WHA) 11. Turkey and Swiss (WTS) 12. Turkey and American (WTA)

So option "D" correctly lists all of Joy's possible sandwich combinations based on the given options.