A digit is a number in the set {0, 1, . . . , 9}. A letter is an element of the
ID: 3042187 • Letter: A
Question
A digit is a number in the set {0, 1, . . . , 9}. A letter is an element of the set{a,b, . . . ,z} {A,B, . . . ,Z}; the first set is the set of lowercase letters and the second is the set of uppercase letters. A special character is an element of the set {#, $, %, &,}.
On Carol’s computer system, a valid password is a sequence of 8 to 12 symbols, where the first symbol is a letter and the remaining symbols are letters or digits. Count the number of possible valid passwords on Carol’s system.
Explanation / Answer
For setting the password of the system we have following possible letters, numbers and character,
Total no of digit = {0, 1, . . . , 9} = 10
Total no of letters = {a,b, . . . ,z} {A,B, . . . ,Z} means
= 26 + 26
= 52
Total no. of character = {#, $, %, &,}.
= 5
valid password is a sequence of 8 to 12 symbols
first symbol is a letter means first letter is fixed we have 51 letters remaining
the remaining symbols are letters or digits means = 51 + 10 = 61 chances for selection of digit or letter
Password would be 8 , 9, 10, 11 or 12 symbols then compute possible arrangments using permutation.
n(P)r. = n ! / ( n - r ) !
n = 61 !
r = 8, 9, 10, 11, or 12
Total possible number = 61(P)8 + 61(P)9 + 61(P)10 + 61(P)11 + 61(P)12
We can find this value using R software :
> install.packages("gtools")
> library(gtools)
> npr <- function(n, r){
return(factorial(n)/factorial(n - r))
}
> Total = npr(61,8)+npr(61,9)+npr(61,10)+npr(61,11)+npr(61,12)
> Total
[1] 8.514717e+20
It is very big value i.e no of way's possible
>>>>>>>>>>>>>> Best Luck >>>>>>>>>>>>>>>>>
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