Question 272662: A computer password consist of six characters.The first two must be lower case letters and the remaining four can be either digits or lower case letters. how many different passwords are possible?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 26 letters in the alphabet.
first 2 must be lower case letters so 26*26 are all possibilities.
remaining 4 can be lower case letters or digits.
10 digits from 0 to 9 makes 26 + 10 = 36 possibilities for each position.
total should be:
26^2 * 36^4 = 1.135420416 * 10^9 possibilities.
that's equivalent to 1,135,420,416 possibilities (1 trillion, 135 billion, 420 million, 416).
to see how this works, use much smaller numbers.
assume 5 positions total
assume first 3 positions can each be one of 2 letters only (a or b).
assume next 2 positions can each be one of 2 letters only plus 1 number (a or b or 1).
possibilities are 2^3 * 3^2 = 8 * 9 = 72
possibilities for the first 3 positions would be:
aaa
bbb
aab
baa
aba
abb
bba
bab
total of 8
possibilities for the next 2 positions would be:
aa
bb
ab
ba
a1
1a
b1
1b
11
total of 9
when you combine the first 3 positions with the last 2 positions, you can get a total of 8 * 9 different possibilities.
example of 2 of the possibilities when you combine the first 3 positions and the last 2 positions would be:
aaaaa
aaabb
aaaab
aaaba
aaaa1
aaa1a
aaab1
aaa1b
aaa11
+
bbbaa
bbbbb
bbbab
bbbba
bbba1
bbb1a
bbbb1
bbb1b
bbb11
+
6 more of these gives you the 8 * 9 total possibilities.
same principle applies to the larger set of numbers in your problem.
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