In class my teacher asked us a question that I don\'t really knowhow to answer.
ID: 2954707 • Letter: I
Question
In class my teacher asked us a question that I don't really knowhow to answer.We were told the food company Chiptole has over 60,000 combinationsof this to choose for their tacos and burritos. She then askedif;
a. Is this claim true or false? Why?
b. How many combinations do they really have?
Chipolte Menu Consists of:
Burrito, Bowl, Soft Tacos, Crispy Tacos, Salad
Choose 1 or 2
chicken, steak, carnitas, barbaco,veggie Meat Portions can be extrameat.
Choost 0,1,or more
rice, fajita veggies, pinto beans, black beans, sour cream, cheese,lettuce, guacamole
Salsas
fresh tomato salsa, roasted chili-corn salsa, tomatillo-green chilisalsa, tomatillo-red chili salsa
Chips+ Salsa
chips, chips and guacamole, chips and fresh tomato salsa, chips androasted chili-corn salsa, chips and tomatillo-green salsa, chipsand tomatillo-red salsa
Drinks
soda(large or small), bottled water, Nantucket Nectar( apple,pinapple orange banana, peach orange, pomegrante cherry), Izze (clementine, blackcherry, grapefruit)
She wants the answer to the number of combinations that can be madewith just the main course and then with the main course and chipsand salsa, and then the final combination with all three.
Explanation / Answer
Main Course So, main course including first 3 things. I skip the first set of selection first, let look at the secondselection That the company got 8 choices on it, they can choose 0,1 or more,maybe 8, i guess. So, combination become 8C0 +8C1 + 8C2 + ...+8C8 = 28 = 256 combination. For Salsas, got 4 choices, and choosing 1, so got 4combination. Let us back to the first 1, it got 5 choices, 4 type of meat andanother one is veggie. They can choose 1 or 2. Case1: When choosing 1 of it Got 4 chance to choose a meat, however, you can decide whether wantto add extra meat. So, here got 4*2 = 8combination 8 Got 1 chances to get veggie, ok, here1. 1 Case2: When choosing of 2 Total is 5C2 = 10, 4 of it are choosing the veggie together with ameat. 4 6 of it are choosing 2 types of meat. For every of it, got 4choices, Both no extra meat, Both extra meat, First meat extra but secondmeat not, First meat no extra but second extra. Example: (chicken and steak no extra)(chicken and steak extrameat)(chicken extra but steak no extra) (chicken no extra but steak extra) So, here got 6 * 4 = 24combination 24 Total here got 37 combination (Look at the bold number) Combination for main course = 37 * 256 * 4 = 37888 combination Main course plus chips and salsas Combination of chips and salsas is 6 So, total combination = 37888 * 6 = 227328 combination Combination of three Drinks combination = 10 Total combination = 227328 * 10 = 2273280
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