- #1
Julian102
- 17
- 1
There are 9 doors in a house.Each door needs a password to open.Passwords can be of at least 4 digits and 10 at most . In how many ways password can be used to open at least one door .
As Andrew posted, this is most unclear. Do you mean, perhaps, that given some set of (presumably distinct) passwords that has been assigned to the doors, how many different passwords would be able to open at least one?Julian102 said:There are 9 doors in a house.Each door needs a password to open.Passwords can be of at least 4 digits and 10 at most . In how many ways password can be used to open at least one door .
haruspex said:As Andrew posted, this is most unclear. Do you mean, perhaps, that given some set of (presumably distinct) passwords that has been assigned to the doors, how many different passwords would be able to open at least one?
If so, it rather depends what lengths of passwords were actually used. It also assumes that a match can arise anywhere in the sequence, e.g. if a given door has the password abcdef then the key abcabcdefx will open it (as well as opening door with password defx).
So, please clarify the question and post an attempt.
True.It came in my exam. You know , sub continental English is quite poor. I provided with the sameandrewkirk said:I'm afraid your question is unclear.
Are you asking how many different possible passwords there are? If so then the number of doors is irrelevant.
Are you asking for the probability that a random sequence of between 4 and 10 digits will open at least one door? If so then 'how many ways' is not the way to ask that question.
Or are you asking something else? If so, what?
There can be (10^4+10^5+...10^10) passwords. Total ways =(10^4+10^5+...10^10 +1) Hence these are the total ways .But we add 1 because there is a way where no password can be used(I forgot to mention in the question...sorry for that). Hence we can open the doors so that at least 1 door is opened in every case. Let x=(10^4+10^5+...10^10 +1)C1+(10^4+10^5+...10^10 +1)C2 + ......+(10^4+10^5+...10^10 +1)C9 = (10^4+10^5+...10^10 +1)^9 - 1andrewkirk said:I'm afraid your question is unclear.
Are you asking how many different possible passwords there are? If so then the number of doors is irrelevant.
Are you asking for the probability that a random sequence of between 4 and 10 digits will open at least one door? If so then 'how many ways' is not the way to ask that question.
Or are you asking something else? If so, what?
This is the number of different possible passwords a door could have, and it includes the option of No Password.Total ways =(10^4+10^5+...10^10 +1)
Let S be the unordered set of all passwords used by the nine doors, where we denote a null password by the word NULL. Note that S has at most nine elements, but may have less if some doors have the same password. S must have at least one element because even if all doors have no password, we have S={NULL}.Let x=(10^4+10^5+...10^10 +1)C1+(10^4+10^5+...10^10 +1)C2 + ......+(10^4+10^5+...10^10 +1)C9
Critical combinatorics problem is a mathematical problem that involves finding the minimum number of elements needed in a set to satisfy certain conditions or properties. It is a subfield of combinatorics, which is a branch of mathematics that studies the ways in which objects can be arranged or selected.
Critical combinatorics problem has various applications in real-world scenarios, such as in computer science, coding theory, and network design. For example, it can be used to determine the minimum number of network nodes needed to ensure reliable communication or the number of error-correcting codes needed to ensure data transmission without errors.
Some common techniques used to solve critical combinatorics problems include generating functions, inclusion-exclusion principle, and graph theory. These techniques help in representing the problem in a mathematical form and finding a solution by using various principles and theorems.
One of the main challenges in solving a critical combinatorics problem is the complexity of the problem, which increases with the size of the problem. As the number of elements and conditions increase, the problem becomes more difficult to solve, and it may require advanced mathematical techniques and algorithms.
Critical combinatorics problem has wide applications in other fields of science, such as biology, economics, and physics. In biology, it can be used to study genetic patterns and population dynamics, while in economics, it can be used to analyze market behavior and resource allocation. In physics, it can be used to study quantum entanglement and statistical mechanics.