How many three-digit passwords are possible on a home security system

Question

How many three-digit passwords are possible on a home security system keypad that consists of all the digits?
A)  10^3 
B) 900
C)  26^3 
D) 26*25*25
E) 10*9*8

P.S.: This question is straight from Veritas course, but it did not have choices. So I have created my own 4 wrong choices here alongwith 1 correct one that Veritas identifies to be so. I have posted it here on the forum to understand why the right answer is right. Please someone make me understand the OA.

GMATinsight · Answer

Password can take any digit from 0 to 9 (i.e. 10 digits) at any place (3 places because of 3 digit password)

i.e. Three places can be filled in 10 * 10 * 10 =  10^3

Answer: option  A

Patronus · Answer

Hi GMATinsight,

The question says it has to be 3 digit number, so should not the first digit just have 9 options than 10?
Likewise, I got 9*10*10 = 900 as the answer.

Can you please explain where did I go wrong?

GMATinsight · Answer

Hi Patronous, You MUST understand the difference between a 3-Digit Number and a 3-Digit password a 3-Digit Number can't have the leftmost digit zero BUT a 3-Digit password can have all digits zero. I hope you can make password of your mobile 0000 type of number as well

Therefore Every Place will have 10 options each to fill then hence the answer must be 10^3 However If the question were how many 3 digit numbers can be made then answer will be 9*10*10 = 900 I hope it clears your doubt!

Bunuel · Answer

Check  Constructing Numbers, Codes and Passwords Questions  in our  Special Questions Directory .

pacifist85 · Answer

Hello,

It is clear. What if the 3-digit passwords should consist of 3 different digits?

Would it then be 10*9*8?

Bunuel · Answer

__________________
Yes.

adityadon · Answer

yes thats correct ... because repetition wont be allowed in that case so 10*9*8

but here nothing is told about it .. so we have 10 choices for each place hence , here , 10*10*10

JeffTargetTestPrep · Answer

Each digit can contain 1 of 10 digits. Thus, the number of ways to create a password is 10 x 10 x 10 = 10^3.

Answer: A

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How many three-digit passwords are possible on a home security system

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