SOLUTION: A password consists of 2 letters followed by a five-digit number. How many passwords are possible if (a) there are no restrictions and (b) none of the letters or digits can

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Question 1156970: A password consists of 2 letters followed by a five-digit number. How many
passwords are possible if
(a) there are no restrictions and
(b) none of the letters or digits can be repeated?
(c) What is the probability of guessing the password in one trial if there are
no restrictions?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A password consists of 2 letters followed by a five-digit number. How many
passwords are possible if
(a) there are no restrictions and
LLDDDDD

26 ways to pick a letter where the first "L" is
TIMES
26 ways to pick a letter where the second "L" is
TIMES
10 ways to pick a letter where the first D is
TIMES
10 ways to pick a letter where the second D is
TIMES
10 ways to pick a letter where the third D is
TIMES
10 ways to pick a letter where the fourth D is
TIMES
10 ways to pick a letter where the fifth D is.

26∙26∙10∙10∙10∙10∙10 = 67600000
(b) none of the letters or digits can be
repeated?
LLDDDDD

26 ways to pick a letter where the first "L" is
TIMES
25 ways to pick a letter where the second "L" is
TIMES
10 ways to pick a letter where the first D is
TIMES
9 ways to pick a letter where the second D is
TIMES
8 ways to pick a letter where the third D is
TIMES
7 ways to pick a letter where the fourth D is
TIMES
6 ways to pick a letter where the fifth D is.

26∙25∙10∙9∙8∙7∙8 = 19656000
(c) What is the probability of guessing the
password in one trial if there are no restrictions?
1 chance in 67600000 or
a probability of 1/67600000.

Edwin