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# A door can be opened using a security code which consists of

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Manager
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A door can be opened using a security code which consists of [#permalink]  21 Apr 2006, 01:14
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A door can be opened using a security code which consists of digits 1,2,3,4. You may press 1,2,3 or 4 buttons or all of them. If to open the door you must press 2 codes, in how many ways can you open the door?
Senior Manager
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Re: PS : Opening a door [#permalink]  21 Apr 2006, 10:06
This is a bit tricky.

If you mean to say that a security code consists of 4 digits, out of 1, 2, 3 and 4, and you need 2 such codes (ie, to press a total of 8 digits) to open the door, you're looking at 4^8 = 65536 codes, or ways to open the door.
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VP
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Re: PS : Opening a door [#permalink]  21 Apr 2006, 10:21
kapslock wrote:
This is a bit tricky.

If you mean to say that a security code consists of 4 digits, out of 1, 2, 3 and 4, and you need 2 such codes (ie, to press a total of 8 digits) to open the door, you're looking at 4^8 = 65536 codes, or ways to open the door.

I am confused too...

If we assume that we need 2 correct codes to open the door, then we have 4 choices each fo rthe other 2 codes. That gives 1*1*4*4 = 16 ways....
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Manager
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I'll wait for a few more responses before I post the answer.
Manager
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Sorry guys..
Has this question really been answered before?
I was just reviewing some of the past posts and stuck in this question.

Is it (4! + 4P3 + 4P2 + 4P1)^2?
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Manager
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2 Digits - 4*3 = 12
3 Digits - 4*3*2 = 24
4 Digits - 4*3*2*2 = 48

Total number of different codes = 84
Manager
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deowl wrote:
(4C1+4C2+4C3+4C4)^2 = 96^2=9216

How come is it combination? Code 4321 and 1234 are two different thing. So I thoght it should be permutations.
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The question is not clear... I'm assuming the code that one types in can have one, two, three or four digits.

Also, a number can be entered more than once In which case, the answer will be (4 + 16 + 64 + 256)^2 = big number.

Else, deowl's is the best answer. Order doesn't matter because you can enter any number, having a max. of 4 digits, and consisting only of 1, 2, 3, and 4.
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