Solution to (a) How many bit strings of length 8 are there? (b) How many bit strings … - Sikademy
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(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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(a) 2^8=256

There are 256 bit strings of length 8.


(b)


2^0+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8=

=2^9-1=511

There are 511 bit strings of length 8 or less.


(c) There are 26 letters in the alphabet.

The number of 6 letter strings =26^6

The number of 6 letter strings without any x =25^6

The number of 6 letter strings with at least one x


26^6-25^6=64775151

There are 64,775,151 strings of 6 lower case English letters that have the letter x in them somewhere.


(d)

Color =12

Gender =2

Size=2

Use the Product Rule


12\cdot2\cdot2=48

48 different types of this shirt are made.



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Question ID: mtid-5-stid-8-sqid-3635-qpid-2334