Question

A password contains exactly 5 letters. How many passwords are possible if letters cannot be used more than once?

Answer 1

@Directrix

Answer 2

65

Answer 3

Why 65? How did you get it?

Answer 4

5*26=130
130/2 = 65

Answer 5

oops

Answer 6

I got 7,893,600

Answer 7

we have \(26\) letters. for the first letter, there are \(26\) possibilities; for the second, having used one letter, there are only \(25\); for the third, then, using similar reasoning, there are \(24\); and so on. the number of possible passwords is then: $$26\cdot25\cdot24\cdot23\cdot22=7893600$$

Answer 8

5= password max
26= numbers of letters in alphabet
130= possibilities including re-occuring numbers
/2 = No re-occurances

Answer 9

A password contains exactly 5 letters.

Are the 5 letters of the password distinct?

And, are the possible passwords all of length 5 letters?

@Daniellelovee

Answer 10

this is also written using factorials as: $$\frac{26\cdot25\cdot24\cdots1}{21\cdots1}=\frac{26!}{(26-5)!}=\ _{26}P_5$$

Answer 11

Correct! @oldrin.bataku

Answer 12

no but oldrin just told me that my answer was correct thank you @Directrix

Answer 13

Nowhere is it said that the passwords have to be of length 5 letters.

letters cannot be used more than once? --> Does not mean the letters are used once.

Answer 14

mhhh true

Answer 15

>A password contains exactly 5 letters.

Okay, I assumed that the password was a specified one. This is a generic any 5 letter password adhering to the conditons.

Yet, do we know that the passwords to be formed from the letters are 5-letter passwords?

Answer 16

is not specified

Answer 17

is my response correct? @Directrix