Question

Assume passwords are 10 characters long, and each character is either a lower case letter, upper case letter, or digit 0, . . . , 9.

(a) How many possible passwords are there?

(b) How many passwords are there with at least one upper case letter, and also never repeat a character?

(c) How many passwords are the same written forwards and backwards?

Answer 1

hre total number of choice for each charecter =26 upper case+26 lower case letter + 10diigts =62

a) total possible passwords =62¹⁰ =8.39*10¹⁷

b) total number of passwords without repetition =⁶²P₁₀ =62*61*60*59*58*57*56*55*54*53=3.90*10¹⁷

total password without repetition and without uppercase =³⁶P₁₀ =36*35*34*33*32*31*30*29*28*27=9.22*10¹⁴

hence passwords with at least one upper case letter, and also never repeat a character

= ⁶²P₁₀ -³⁶P₁₀ =3.90*10¹⁷-9.22*10¹⁴ =3.89*10¹⁷

c)

for same forward and back ward spell ; we need to select only first 5 lettter as other 5 should match first 5.

hence number of passwords =62⁵ =916132832