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805+ Level|   Combinations|      
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Bunuel
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A combination lock is set to open when the correct direction sequence 27 Nov 2022, 11:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

23% (01:35) correct 77% (01:43) wrong based on 109 sessions

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A combination lock is set to open when the correct direction sequence is selected, either left-right-left or right- left-right, and when the correct three numbers from 1 to 60,inclusive,are selected in the correct order. If each number can be used only once, which of the following gives the number of different combinations that can be set to open the lock?

A. (30)(59)(58)
B. (60)(60)(60)
C. (60)(59)(58)
D. 2(60)(60)(60)
E. 2(60)(59)(58)
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C
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A combination lock is set to open when the correct direction sequence 11 Mar 2023, 08:21
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from my understanding of the question the total ways possible will be one only because the lock shall open only when correct direction sequence is selected, so only one possible way

60*59*58
option C

Bunuel please check OA

Bunuel
A combination lock is set to open when the correct direction sequence is selected, either left-right-left or right- left-right, and when the correct three numbers from 1 to 60,inclusive,are selected in the correct order. If each number can be used only once, which of the following gives the number of different combinations that can be set to open the lock?

A. (30)(59)(58)
B. (60)(60)(60)
C. (60)(59)(58)
D. 2(60)(60)(60)
E. 2(60)(59)(58)
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A combination lock is set to open when the correct direction sequence 11 Mar 2023, 09:33
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Archit3110
from my understanding of the question the total ways possible will be one only because the lock shall open only when correct direction sequence is selected, so only one possible way

60*59*58
option C

Bunuel please check OA

Bunuel
A combination lock is set to open when the correct direction sequence is selected, either left-right-left or right- left-right, and when the correct three numbers from 1 to 60,inclusive,are selected in the correct order. If each number can be used only once, which of the following gives the number of different combinations that can be set to open the lock?

A. (30)(59)(58)
B. (60)(60)(60)
C. (60)(59)(58)
D. 2(60)(60)(60)
E. 2(60)(59)(58)
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_____________________________________
Fixed the OA.
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A combination lock is set to open when the correct direction sequence 12 Mar 2023, 03:22
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I am confused. Whether correct combination here means only the combination of numbers an doesn't include the direction ?

Question is : either left-right-left or right- left-right, and when the correct three numbers from 1 to 60

If direction and sequence of 3 numbers both constitute a combination then we should factor the OR condition in the direction and the answer should be = 2*60*59*58

Kindly clarify..
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A combination lock is set to open when the correct direction sequence 30 Jul 2023, 04:12
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But what about the left-right-left and right-left-right? Wont there be 2 ways to reach a particular pattern?



Archit3110
from my understanding of the question the total ways possible will be one only because the lock shall open only when correct direction sequence is selected, so only one possible way

60*59*58
option C

Bunuel please check OA

Bunuel
A combination lock is set to open when the correct direction sequence is selected, either left-right-left or right- left-right, and when the correct three numbers from 1 to 60,inclusive,are selected in the correct order. If each number can be used only once, which of the following gives the number of different combinations that can be set to open the lock?

A. (30)(59)(58)
B. (60)(60)(60)
C. (60)(59)(58)
D. 2(60)(60)(60)
E. 2(60)(59)(58)
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A combination lock is set to open when the correct direction sequence 30 Jul 2023, 09:45
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there are 2 ways to reach a particular pattern but its still only 1 pattern. for example, 12-23-34 can be reached by keying in 12,23,34 from left to right. or using 34,23,12 from right to left. still the pattern in the same and we should only count once. so archit soln seems to be right.

turbosea
But what about the left-right-left and right-left-right? Wont there be 2 ways to reach a particular pattern?



Archit3110
from my understanding of the question the total ways possible will be one only because the lock shall open only when correct direction sequence is selected, so only one possible way

60*59*58
option C

Bunuel please check OA

Bunuel
A combination lock is set to open when the correct direction sequence is selected, either left-right-left or right- left-right, and when the correct three numbers from 1 to 60,inclusive,are selected in the correct order. If each number can be used only once, which of the following gives the number of different combinations that can be set to open the lock?

A. (30)(59)(58)
B. (60)(60)(60)
C. (60)(59)(58)
D. 2(60)(60)(60)
E. 2(60)(59)(58)
Show more
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A combination lock is set to open when the correct direction sequence 30 Jul 2023, 10:45
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Bunuel
A combination lock is set to open when the correct direction sequence is selected, either left-right-left or right- left-right, and when the correct three numbers from 1 to 60,inclusive,are selected in the correct order. If each number can be used only once, which of the following gives the number of different combinations that can be set to open the lock?

A. (30)(59)(58)
B. (60)(60)(60)
C. (60)(59)(58)
D. 2(60)(60)(60)
E. 2(60)(59)(58)
Show more


Say the code is 1-2-3. You need to get to 1 by rotating the dial left (clockwise) to reach 1, then right (counter clockwise) to reach 2 and then left to reach 3 OR the reverse, i.e. first right, then left and then right.
Thus, even if someone selected the correct numbers, the person would still have to get the above sequence correct, else the lock won't open.
For example, if someone uses the sequence L-L-L, it won't open. However, it is already known that the sequence is either L-R-L or R-L-R. Thus, while trying the sequence, someone would definitely use any one of those two. So, that information is redundant.
Thus, essentially, it is only about the choice of the 3 numbers in the correct order i.e., 60 * 59 * 58 ways

Note: To understand better, say, we have to key-in a password using the letters C, A, T, and while making the input, we can either use all caps or all small, both would be counted as equivalent passwords. To count the number of options, we will simply say CAT, CTA, ACT, ATC, TAC, TCA. We won't count the other case of all small since that is anyways equivalent to these 6. Thus, the answer is simply 3 * 2 * 1 = 6

Answer C
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A combination lock is set to open when the correct direction sequence 14 Jul 2025, 03:03
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