Ok, I swear either I just don't get it, or the back of the book is wrong. But here's the question. A person can eat a meal that consists of one main course, one vegetable dish, and two different desserts. He can choose from 10 main dishes, 8 vegetable dishes, and 13 desserts. How many meals are possible? The answer I keep getting is 12,840 but the book has 6420. Can anybody give me a step by step? Thanks and good luck
2007-01-18 17:15:28 · 3 answers · asked by speedywest16 3 in Science & Mathematics ➔ Mathematics
Choices are independent, so you'll multiply.
main: 10 choices
veg: 8 choices
2 different desserts out of 13 is 13C2 ( that's choosing 2 out of 13 without replacement and without regard to order)
13C2 = 13*12/2 = 13*6 = 78
Now, let's multiply
10*8*78 = 6240
Your error was in how you chose the desserts, most likely.
2007-01-18 17:27:47 · answer #1 · answered by modulo_function 7 · 0⤊ 0⤋
10 x 8 x 13 x 12...
My English is not that good for explaining math...
10 is for the main course probabilities..
8 is for the veg dish
13 is for the dessert..
12 is for another dessert.. It's from 13-1.. Because one of the dessert is already taken...
I hope you can understand my explaination
2007-01-19 01:35:19 · answer #2 · answered by andru 2 · 1⤊ 0⤋
The answer is
C(10,1)*C(8,1)*C(13,2) = 10*8*[(13*12)/2] = 6240
It doesn't matter which order the two desserts are chosen in. If you just say 13*12 you are specifying order. You needed to divide by 2.
2007-01-19 01:30:30 · answer #3 · answered by Northstar 7 · 0⤊ 0⤋