Question 153019
1) Here's a good question: is the password "pass" different from "ssap"? Since it is, this means that order matters. 



Since order does matter, we must use the <a href=http://www.mathwords.com/p/permutation_formula.htm>permutation formula</a>:



*[Tex \LARGE \textrm{_{n}P_{r}=]{{{n!/(n-r)!}}} Start with the permutation formula




*[Tex \LARGE \textrm{_{26}P_{5}=]{{{26!/(26-5)!}}} Plug in {{{n=26}}} and {{{r=5}}}




*[Tex \LARGE \textrm{_{26}P_{5}=]{{{26!/21!}}} Subtract {{{26-5}}} to get 21




Expand 26!
*[Tex \LARGE \textrm{_{26}P_{5}=]{{{(26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)/21!}}}




Expand 21!
*[Tex \LARGE \textrm{_{26}P_{5}=]{{{(26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)/(21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)}}}




*[Tex \LARGE \textrm{_{26}P_{5}=]{{{(26*25*24*23*22*cross(21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1))/(cross(21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1))}}}  Cancel




*[Tex \LARGE \textrm{_{26}P_{5}=]{{{26*25*24*23*22}}}  Simplify





*[Tex \LARGE \textrm{_{26}P_{5}=]{{{7893600}}}  Now multiply 26*25*24*23*22 to get 7,893,600


So there are 7,893,600 possible passwords



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2)


If order does matter, then the number of combinations is {{{8!=8*7*6*5*4*3*2*1=40320}}}


So there are 40,320 ways to rearrange the books



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3)


Let's say that the format is 


(555)-xxx-xxxx


So we have 7 slots we're dealing with. This means that {{{r=7}}}. Since we have 10 numbers to choose from, this tells us that {{{n=10}}} (note: the "26" that you used implies that you'll be using letters). Also, because order matters, we must use the <a href=http://www.mathwords.com/p/permutation_formula.htm>permutation formula</a>:



*[Tex \LARGE \textrm{_{n}P_{r}=]{{{n!/(n-r)!}}} Start with the permutation formula




*[Tex \LARGE \textrm{_{10}P_{7}=]{{{10!/(10-7)!}}} Plug in {{{n=10}}} and {{{r=7}}}




*[Tex \LARGE \textrm{_{10}P_{7}=]{{{10!/3!}}} Subtract {{{10-7}}} to get 3




Expand 10!
*[Tex \LARGE \textrm{_{10}P_{7}=]{{{(10*9*8*7*6*5*4*3*2*1)/3!}}}




Expand 3!
*[Tex \LARGE \textrm{_{10}P_{7}=]{{{(10*9*8*7*6*5*4*3*2*1)/(3*2*1)}}}




*[Tex \LARGE \textrm{_{10}P_{7}=]{{{(10*9*8*7*6*5*4*cross(3*2*1))/(cross(3*2*1))}}}  Cancel




*[Tex \LARGE \textrm{_{10}P_{7}=]{{{10*9*8*7*6*5*4}}}  Simplify





*[Tex \LARGE \textrm{_{10}P_{7}=]{{{604800}}}  Now multiply 10*9*8*7*6*5*4 to get 604,800



So there are 604,800 unique phone numbers to choose from.