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A to-go restaurant is running a special where customers can choose
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18 Jul 2022, 00:32
18 Jul 2022, 00:32
Expert Reply
00:00
Question Stats:
75% (01:17) correct
25% (00:53) wrong based on 24 sessions
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A to-go restaurant is running a special where customers can choose from among 10 dishes to make up a takeout box with 5 choices. The manager finds that the number of different boxes possible is:
A 50
B 252
C 1200
D 30,240
E 3,628,800
A 50
B 252
C 1200
D 30,240
E 3,628,800
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
Re: A to-go restaurant is running a special where customers can choose
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20 Jul 2022, 09:40
20 Jul 2022, 09:40
1
Expert Reply
OE
Quote:
The question to answer is “How many groups of 5 can be made from 10 choices?” This is a combination problem, since there is no order to the choices. There are 10 choices for the first slot, 9 choices for the second, 8 for the third, 7 for the fourth, and 6 for the fifth, so 10 ⋅ 9 ⋅8 ⋅ 7 ⋅ 6 = 30,240. Next, divide by the factorial of the number of slots: 5! = 5 ⋅ 4 ⋅ 3 ⋅ 2 = 120, so 30,240/120 = 252.
A to-go restaurant is running a special where customers can choose
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09 Sep 2022, 02:47
09 Sep 2022, 02:47
1
A to-go restaurant is running a special where customers can choose from among 10 dishes to make up a takeout box with 5 choices. The manager finds that the number of different boxes possible is:
This is a combinations problem because the order of the dishes in the takeout box does not matter.
Thus the number of different boxes possible is \(10C5 = 10!/(10-5)! * 5! = 252\)
Here, one can quickly calculate:
We have,
10 * 9 * 8 * 7 * 6/5!
10 * 9 * 8 * 7 * 6/120
Here 10 * 9 * 8 = 720 and when 720 is divided by 120 we get 6. Then we multiply this 6 with 42 (6 * 7), and we will get 252 as the answer.
Or just estimate 720/100 = 7.2 and you know that 7.2 * 42 will be around 280 to 300 and since you divided by 100 instead of 120, the answer should be less than 280 - 300, but in and around the 200s, so the answer should be 252. The fact that no other answer choice is near this range should help you to choose this (252) as the correct answer choice.
This is a combinations problem because the order of the dishes in the takeout box does not matter.
Thus the number of different boxes possible is \(10C5 = 10!/(10-5)! * 5! = 252\)
Here, one can quickly calculate:
We have,
10 * 9 * 8 * 7 * 6/5!
10 * 9 * 8 * 7 * 6/120
Here 10 * 9 * 8 = 720 and when 720 is divided by 120 we get 6. Then we multiply this 6 with 42 (6 * 7), and we will get 252 as the answer.
Or just estimate 720/100 = 7.2 and you know that 7.2 * 42 will be around 280 to 300 and since you divided by 100 instead of 120, the answer should be less than 280 - 300, but in and around the 200s, so the answer should be 252. The fact that no other answer choice is near this range should help you to choose this (252) as the correct answer choice.
