Possible ways tp open the door (Permutation/Combination)

Question

A door can be opened only with a security code that consists of five
buttons: 1, 2, 3, 4, 5. If, to open the door you must press three codes, then how many possible ways are there to open the door? Assume that the same code may be repeated.

alpha_plus_gamma · Answer

I assume this means that each code consists of 5 digits. Then there are 5!= 120 codes possible.

120*120*120 ways

DenisSh · Answer

The number of possible ways to open the door
P (n, k) =  \frac{n!}{(n - k)!} ,
so P (5, 3) =  \frac{5!}{2!} = 3 * 4 * 5 =   60

nitindas · Answer

It should be 5!*5!*5! = 120 ways

sandipchowdhury · Answer

As same codes can be repeated 
my answer is =5*5*5= 125

DaveGG · Answer

Disagree: you have 5! possibilities each time you type in a code (having the same code purely means you don't have to subtract duplicates which makes the question easier). Thus 5! x 5! x 5! is the correct answer.

shkusira · Answer

Ok now my take seems to be completely different on this one. Plz point out the flaw if any:

Since there are 5 numbers in a given code and there are 5 numbers, I think the total posssible codes are: 5*5*5*5*5 = 3125. No where in the question does it say that you are not allowed to repeat the same digit in the code.

Now since the codes can be repeated, 3125 is the number of code possible without combination. We will have to add this figure to the one possible with combination.

Now to select 3 codes out of 3125, we should use the combination formula. C(3125, 3). Now this yields a huge figure ( 3123*3124*3125)/6

This should be added to the prev figure, ie, total possibilities:
3125 + ( 3123*3124*3125)/6.

Now my concern is the magnitude of the solution. Rarely do I see such an insane answer.

Please provide the official answer and if someone can point out any flaw in the reasoning above, please let me know.

walker · Answer

5 possibilities for each pressed button: 5*5*5=125 ways.
The problem is poorly written or I don't understand how to press three codes that consist of five buttons: 
1) "a security code that consists of five buttons" - a code cannot consists of 5 buttons, can it?
2) "must press three codes" - maybe buttons?

kbulse · Answer

May be one must press 3 buttons out of 5 simultaneously to open the door:)

So it is 5*4*3=60

shkusira · Answer

That makes it really easy and somewhat possible for the GMAT.

What I thought was:

1 code = 5 buttons
Therefore 3 codes = 15 Buttons.

Hence I gave that long explanation.

I am still unsure of its veracity but can someone tell me the flaw in that one? Also, OA plz

Possible ways tp open the door (Permutation/Combination)

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