Math Is Fun Forum

gracenalec

Member

Registered: 2006-01-23

Posts: 4

Door secret code...permutation

A secret code that needs to be key-ed in using only 1,2,3,4,5 button. If to open the door, u need to press three buttons, how many possible ways there to open the door? Assume tat the same code may be repeated.

For now, i have to ways in mind...it's either

5 x 5 x 5

OR

1st condition- all numbers are different = 5p3
2nd condition- 2 num r de same, 1 is diff = (3p3/2p2) x 4
3rd condition- all num r de same = (3p3/3p3)

and add all the answers together..

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i'm nt sure which would b a better way..or the correct way..pls help..

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Door secret code...permutation

If the code can be repeated, then the answer is 5³ as you say.

Just like there are 10³ possible decimal numbers between 000 and 999

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman