Question 950549
1.	A password must be 6, 7, or 8 characters long, and may include capital
letters, lower-case letters, or digits. In how many ways could this be done        
		     
a.	with no restriction?
<pre>
26 capital letters + 26 lower case letters + 10 digits = 62 characters

62^6 + 62^7 + 62^8 = 221918520426688  
</pre>
b.	with no repetition permitted?
<pre>
62P6 + 62P7 + 62P8 = 138848807594160
</pre>
c.	if at least one of the characters in part a) must be a digit?
<pre>
That will be the answer to (a) minus the number with no digits.

With no digits:

26 capital letters + 26 lower case letters = 52 characters

52^6 + 52^7 + 52^8 = 54507570843648

Subtracting from the result of part (a)

221918520426688 - 54507570843648 = 167410949583040

Edwin</pre>