Combinations question/someone please help

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Nerdygeek12
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#1
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A spy is trying to open a security door by entering the correct code into a key pad. The
key pad has 10 buttons (for the digits 0; 1; : : : ; 9). How many possible codes does she have
to try at most if...

(a) ...she only knows that the correct code is 4 digits long? I think this is 10!/10C4
(b) ...she knows that the correct code consists of 4 distinct digits?
(c) ...she knows which 4 distinct digits are involved in the correct code?
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old_engineer
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(Original post by Nerdygeek12)
A spy is trying to open a security door by entering the correct code into a key pad. The
key pad has 10 buttons (for the digits 0; 1; : : : ; 9). How many possible codes does she have
to try at most if...

(a) ...she only knows that the correct code is 4 digits long? I think this is 10!/10C4
(b) ...she knows that the correct code consists of 4 distinct digits?
(c) ...she knows which 4 distinct digits are involved in the correct code?
For part (a) would your reasoning work if there was only one button? Maybe start by considering how many possible codes there would be for one button, then two buttons.
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Nerdygeek12
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(Original post by old_engineer)
For part (a) would your reasoning work if there was only one button? Maybe start by considering how many possible codes there would be for one button, then two buttons.
I don't understand?
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Nerdygeek12
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(Original post by old_engineer)
For part (a) would your reasoning work if there was only one button? Maybe start by considering how many possible codes there would be for one button, then two buttons.
Is it like 10!/4!*3!*2!*1!
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old_engineer
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(Original post by Nerdygeek12)
I don't understand?
Sorry, I may have added confusion by using the word button in the wrong context. If there are ten buttons (as in the question) but the code consists of just one number, how many possible codes are there?
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old_engineer
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(Original post by old_engineer)
Sorry, I may have added confusion by using the word button in the wrong context. If there are ten buttons (as in the question) but the code consists of just one number, how many possible codes are there?
I'm trying not to labour the point, but if the code was just one digit long, the possible codes would be 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9, i.e. there are ten possible codes. Now, if the code was two digits long, the possible codes would be 00, 01, 02 etc all the way up to 99. How many possible codes is that? And can you now extend the reasoning to the case where the code consists of four digits?
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