Can you all explain how you got the answers to the problems, I'm having trouble getting the right answer, thanks. Example A: At a certain ice cream parlor, customers can choose among five different ice cream flavors and can choose either a sugar cone or a waffle cone. Considering both ice cream flavor and cone type, how many distinct triple-scoop cones with three different ice cream flavors are available? Example B: If the price of gasoline increases by 25% and Maria intends to spend only 15% more on gasoline, by what % should she reduce the quantity of gas that she buys?
i don't know the answer, but I'm craving ice cream now. my shot at A: 5 different ice creams x 2 diff cones x 3 different scoops =30 combinations
the answer to example A is 20 - my response was 120, (5x4x3) x 2 the answer to example B is 8% but have no clue how they got those answers
Try it with 'real' numbers: Gas costs $1 a unit. It goes up to $1.25. Maria spends $1.15. She can therefore buy 1.15/1.25 of a unit, which is 0.92, rather than a whole unit. Her reduction is 1 - 0.92, or 8%.
For A: They did 5 Combination 3, which is equal to 5!/3!2! = 10 for the scoops themselves. Then multiply by 2 for the cones to get 20. The reason you can't do just 5x4x3 is because order then matters. Getting scoops A,B,C and A,C,B in your case are different, but for the problem's sake it isn't. For B, do an example case. Pretend gas was originally 1 dollar a gallon and she bought 1 gallon (so she spends one dollar). Later gas became 1.25, and she's willing to spend 1.15. So she's willing to buy 1.15/1.25 of the gas. The percentage decrease is calculated by (1.25-1.15)/1.25 = .10/1.25 = .08 or 8 percent.
A is an elementary statistics problem having to do with Permutations and combinations. i.e. an ordered series. It is easier to calculate without repetition, Your answer is incorrect because you are not taking into consideration redundancy (i.e. chocolate / vanilla / strawberry is the same as strawberry / vanilla / chocolate). So in this case you do 5 different flavors minus the number of choices you need to put in a series which is 3. If there was no requirement for an order of 3 scoops, You would simply multiply 5 * 5 * 2 in normal circumstances and get an answer of 50 different combinations. But in this case you must subtract 5*3*2 because you are only left with 2 choices since 3 out of 5 must be selected. 5*5*2 = 50 different combinations (25 flavors * 2 cones) subtract 5*3*2 = (15 flavors * 2 cones) Basically this means 15 out of the 25 combinations are redundant, therefore you can only have 10 distinct combinations of flavors for a 3 scoop cone. Now multiply that by the 2 choices for cones and your answer is 20.
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ths balla, you have to try yourself. Like moes said, the problem B is a permutation AND combination problem. Read the 'combination' section here: http://www.omegamath.com/Data/d2.2.html P is the formula for combination. Good luck, sir.
To simplify A, if you're five flavors are A,B,C,D and E, your 3 scoop combinations become: 1. ABC 2. ABD 3. ABE 4. ACD 5. ACE 6. ADE 7. BCD 8. BDE 9. BCE 10. CDE All other combinations are variants of the above. 10 combinations, times 2 cone choices, equals 20 options. To simplify B, before she was spending $1 for 1 gallon. Now 1 gallon costs $1.25, but she is only willing to buy $1.15 worth of gas. So Maria will buy $1.15 / $1.25 of a gallon. $1.15 is an 8% discount off $1.25.
What does it matter? Her demand for gasoline is inelastic. When she runs out, she has to go buy more. What she needs to do is change her driving habits so that she either goes to fewer places, gets there more efficiently, or more often takes alternate modes of transportation. She can't change her consumption by merely buying less at a time!
