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April 20th, 2014, 10:16 PM   #1
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"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?
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April 20th, 2014, 11:31 PM   #2
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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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