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.
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