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<pre>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</pre>(b) none of the letters or digits can be
repeated?<pre>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</pre>(c) What is the probability of guessing the
password in one trial if there are no restrictions?<pre>1 chance in 67600000 or
a probability of 1/67600000.

Edwin</pre>