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Consider passwords of length 8 using symbols from the set of lower case letters: {a, b,...

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Physics

Consider passwords of length 8 using symbols from the set oflower case letters: {a, b, c, ..., z}.

(a) How many such passwords use the letter p exactlytwo times and the letter q exactly two times? Toillustrate, both akpqbqop and quaqpoop satisfythis condition. Include a brief indication of your strategy.

(b) How many such passwords use the letter p exactlyonce and the letter q exactly once and also have lettersarranged so the p is not nextto the q? To illustrate, we want to countpasswords like amkquoop but not moopguzz orwhaqpodo since these have the symbol p next tothe q. Include a brief indication of your strategy.

Answer & Explanation Solved by verified expert
4.2 Ratings (575 Votes)
a For a password that contains p exactly 2 times and qexactly 2 times this means that the other 4 letters of thepassword are made of the 24 other letters ie the alphabet notincluding p and qHow many 4 letter passwords can we make with 24 lettersThis is given by becausethere are 24 choices for each of the four places in thepasswordNow how can we add the ps and qs into each of thesechoicesNow let us place the two letter ps into    See Answer
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