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April 20th, 2014, 10:16 PM  #1 
Senior Member Joined: Nov 2011 Posts: 101 Thanks: 0  "how many" questions
1. how many ordered lists with entries from {1, 2, 3, 4, 5, 6} of length 3 are there? answer  216 2. a certain state has a simple rule for its license plates: use two letters followed by four digits. how many possible plates are there? answer  6,760,000 3. we will represent the results of ten tosses of a coin as an ordered list of length 10 with entries from {H,T}. how many different results are possible? answer  1,024 4, A password has six numbers, each in the range 1 to 9. how many different passwords are there? answer  531,441 can anyone show me how you get this answers? 
April 20th, 2014, 11:31 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 
1.) You have 6 choices for each of the 3 elements, hence: $\displaystyle N=6\cdot6\cdot6=216$ 2.) You have 26 choices for the first two elements and 10 choices for the next 4 elements, hence: $\displaystyle N=26^2\cdot10^4=6760000$ 3.) You have 2 choices for each of the 10 elements, hence: $\displaystyle N=2^{10}=1024$ 4.) You have 9 choices for each of the 6 elements, hence: $\displaystyle N=9^6=531441$ 

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