A question about combinatorics

[Albi]

A password contains 4 different digits from 0 to 9.How many different passwords must I try to find the correct one?

 

[Deleted member 4993]

A password contains 4 different digits from 0 to 9.How many different passwords must I try to find the correct one?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[pka]

A password contains 4 different digits from 0 to 9.How many different passwords must I try to find the correct one?

Answer HERE

 

[Dr.Peterson]

A password contains 4 different digits from 0 to 9.How many different passwords must I try to find the correct one?

How many ways are there to choose the first digit in the password?

How many ways to choose the second?

Then, how many ways does that make to choose just the first two digits?

Continue like that.

 

[Albi]

How many ways are there to choose the first digit in the password?

How many ways to choose the second?

Then, how many ways does that make to choose just the first two digits?

Continue like that.

This is definitely an option but pka has a much shorter one.Thank you for taking the time to help!

 

[Dr.Peterson]

This is definitely an option but pka has a much shorter one.Thank you for taking the time to help!

Actually, his answer is identical to mine; it looks shorter only because he gave you the answer without asking you to think!

My answer is very quickly calculated as [MATH]10\times9\times8\times7 = 5040[/MATH], which is another way to calculate [MATH]_{10}P_4[/MATH].

Of course, you can do it more quickly using the permutation notation if you are familiar with it, and have a calculator that will do it for you. You've given no indication how much you know about permutations, so I assumed from the level of the question that you might not.

 

[Albi]

Actually, his answer is identical to mine; it looks shorter only because he gave you the answer without asking you to think!

My answer is very quickly calculated as [MATH]10\times9\times8\times7 = 5040[/MATH], which is another way to calculate [MATH]_{10}P_4[/MATH].

Of course, you can do it more quickly using the permutation notation if you are familiar with it, and have a calculator that will do it for you. You've given no indication how much you know about permutations, so I assumed from the level of the question that you might not.

Then why would I mention combinatorics in the title if I would have not known what permutations are

 

[pka]

Then why would I mention combinatorics in the title if I would have not known what permutations are

At the university from which I retired ten+ years ago, the socalled sciences were divided into three divisions: Physical Sciences, Biological Sciences & Mathematical Sciences. At a chairs meeting with the dean, I introduced the beta version of WolfranAlpha. I proposed becoming a testing site. Well that did not fly. The chemistry chair thought having a program able to draw all organic compounds would destroy his course. The dean, a biologist, agreed. I think it ironic that the current changeover to online instruction makes such programs essential.
I predict that in ten years no basic calculus text books will have the topic techniques of integration in it.
Think about it: how many students are taught how to find \(\sqrt{13}~?\)