(a) How many bit strings of length 8 are there? (b) How many bit strings of length 8 or less are there? (Count the empty string of length zero also.) (c) How many strings of 6 lower case English letters are there that have the letter x in them somewhere? Here strings may use the same letter more than once. (Hint: It might be easier to first count the strings that don't have an x in them.) (d) A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes in 2 sizes for each sex. How many different types of this shirt are made?
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There are 256 bit strings of length 8.
There are 511 bit strings of length 8 or less.
(c) There are 26 letters in the alphabet.
The number of 6 letter strings
The number of 6 letter strings without any x
The number of 6 letter strings with at least one x
There are 64,775,151 strings of 6 lower case English letters that have the letter x in them somewhere.
Use the Product Rule
48 different types of this shirt are made.