Question
I have tried this several ways, with no luck. I assumethere are either a total of 44 combinations (10+8+13+13) or 43total (10+8+13+12). I then take the 43! / (43-4)!4!. The 4 is for the 4 different components of the meal (one main dish,one vegetable, and two deserts). The answer should be6240. I don't understand how to set this up correctly. Is it31 total (10+8+13)? I don't understand this problem from thebegining. Page 178, problem #19 states: Space shuttle astronauts each consume an average of 3000calories per day. One meal normally consists of a main dish,a vegetable dish, and two different desserts. The astronautscan shoose from 10 main dishes, 8 vegetable dishes, and 13desserts. How many different meals are possible? Thanks, Kevin I have tried this several ways, with no luck. I assumethere are either a total of 44 combinations (10+8+13+13) or 43total (10+8+13+12). I then take the 43! / (43-4)!4!. The 4 is for the 4 different components of the meal (one main dish,one vegetable, and two deserts). The answer should be6240. I don't understand how to set this up correctly. Is it31 total (10+8+13)? I don't understand this problem from thebegining. Page 178, problem #19 states: Space shuttle astronauts each consume an average of 3000calories per day. One meal normally consists of a main dish,a vegetable dish, and two different desserts. The astronautscan shoose from 10 main dishes, 8 vegetable dishes, and 13desserts. How many different meals are possible? Thanks, Kevin
Explanation / Answer
You can choose 1 from 10 main dishes, 1 from 8 veggie dishes,and 2 from 13 desserts. Thus, the answer is: C(10,1)*C(8,1)*C(13,2)=10*8*13*12/2=10*8*78=6240. First of all, you cannot add these combinations up. Youmust multiply them. It's just like a situation where you have2 balls and 3 mice to choose from. There aren't 2+3combinations, there are 2*3 combinations because for every ballthere are 3 mice to choose. Secondly, If you take one desert away, you would only have 12left. Then, you would have to multiply 13*12 for the samereason as the last question. However, you have to divide by 2because there are two different ways you can choose those 2desserts from the 13: you can choose the chocolate cake andthen the apple pie or choose the apple pie and then the chocolatecake.