If upper and lower case letters in a 6 letter passwords

[wind]

Hi, can someone hwlp me with this question?

If upper and lower case letters are considered as different letters, how may 6 letter passwords are possible if

a) there are no repeating letters
b) with at least one capital


a)

52*51*50*49*48*47
=14 658 134 400

but the answer is 19 770 609 664

b)

26C1*26C5
26C2*26C4
26C3*26C3
26C4*26C2
26C5*26C1
26C6*26C0

=19 799 390

but the answer is 19 461 693 888


Thanks

 

[pka]

I agree with you about part a.
You really have had trouble with that answer key!

 

[wind]

lol, thanks Pka

 

[pka]

For part (b) take the total of all lower case passwords from the total.
\(\displaystyle P(52,6) - P(26,6)\)