SOLUTION: I would like your opinion on the following problem: A password is composed of 4 different letters (out of 26 upper case letters) and 2 different digits (out of 10 digits from 0 t

Algebra.Com
Question 854962: I would like your opinion on the following problem:
A password is composed of 4 different letters (out of 26 upper case letters) and 2 different digits (out of 10 digits from 0 to 9).
How many arrangements are possible?
This my attempt so far.
Attempt 1:
26 x 25 x24 x23 x 10 x 9
Attempt 2:
26C4 x 9C2 x 6

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
4 different letters and 2 different digits.

if you assumed that the same letter could not be used more than once in the password then you would be correct.

the solution would then be:

26*25*24*23*10*9 which is the same as 26P4*10P2

26P4 is 26*25*24*23
10P2 is 10*9

the combination formula would not be correct since 26C4 = 26*25*24*23 / 1*2*3*4 and 10C2 = 10*9 / 1*2
this is not what you want.

if, however, you allow the same letter to be used in more than one position and the same number to be used in more than one position, then the solution would be:

26*26*26*26*10*10 which could also be written as 26^4*10^2





RELATED QUESTIONS

7.A spyware is trying to break into a system by guessing its password. It does not give... (answered by edjones)
Assume that a password to log onto a computer account is to consist of any 4 digits or... (answered by richwmiller)
I am trying to figure out what formula to use on this question and also how to proceed... (answered by Alan3354,josmiceli)
Please show me specific detailed answers to these question i got wrong on my test.... (answered by ewatrrr)
How many possible eight character passwords can be created using only uppercase letters... (answered by sudhanshu_kmr)
I need help in probabilities the question is: You must make a password for your email... (answered by Boreal,solver91311)
Please help me solve this problem. The topic is probability. A password consists of a... (answered by greenestamps,richwmiller)
Supposed your computer password must contain four characters, must begin with a letter,... (answered by ikleyn)
Please help me solve the two questions: 1.A person selects 3 letters randomly from 26... (answered by stanbon)