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How many possible combinations can a 3-digit safe code have?
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07 May 2019, 10:09
07 May 2019, 10:09
Expert Reply
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Question Stats:
52% (00:16) correct
47% (00:22) wrong based on 40 sessions
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How many possible combinations can a 3-digit safe code have?
(A) \(9C_3\)
(B) \(9P_3\)
(C) \(3^9\)
(D) \(9^3\)
(E) \(10^3\)
(A) \(9C_3\)
(B) \(9P_3\)
(C) \(3^9\)
(D) \(9^3\)
(E) \(10^3\)
Re: How many possible combinations can a 3-digit safe code have?
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09 May 2019, 00:38
09 May 2019, 00:38
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Could it be 10C3?
Re: How many possible combinations can a 3-digit safe code have?
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10 May 2019, 02:52
10 May 2019, 02:52
Expert Reply
The safe combination could be 433 or 334; the combinations are the same, but their ordering is different.
Order is important for the safe combinations, this is a permutation problem.
A safe code can be made of any of the numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. No two objects in the set are indistinguishable. Hence, the base set does not have any indistinguishable objects.Repetitions of numbers in the safe code are possible. For example, 334 is a possible safe code.
Hence, the problem is a permutation, with repetition and no indistinguishable objects.
Moreover, the first digit has an additional rule: it cannot be 0 (because in this case the number would actually be 2-digit number).
Hope this helps.
Regards
Order is important for the safe combinations, this is a permutation problem.
A safe code can be made of any of the numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. No two objects in the set are indistinguishable. Hence, the base set does not have any indistinguishable objects.Repetitions of numbers in the safe code are possible. For example, 334 is a possible safe code.
Hence, the problem is a permutation, with repetition and no indistinguishable objects.
Moreover, the first digit has an additional rule: it cannot be 0 (because in this case the number would actually be 2-digit number).
Hope this helps.
Regards
