SOLUTION: 1. Suppose you use five different letters to make a computer password. Find the number of possible five letter passwords. I got 11,881,376 using the formula 26 C 5. Is this co

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: 1. Suppose you use five different letters to make a computer password. Find the number of possible five letter passwords. I got 11,881,376 using the formula 26 C 5. Is this co      Log On

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Question 153019: 1. Suppose you use five different letters to make a computer password. Find the number of possible five letter passwords.
I got 11,881,376 using the formula 26 C 5. Is this correct?
2. How many different ways can someone arrange 8 books on a shelf? I got 64.
3. If the first three digits of someone's phone number (no area code) are 555, how many different phone numbers could they have? I got 11,881,373
I used 26 to the 5th power.
Thanks for your help.

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
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 permutation formula:


n%21%2F%28n-r%29%21 Start with the permutation formula



26%21%2F%2826-5%29%21 Plug in n=26 and r=5



26%21%2F21%21 Subtract 26-5 to get 21



Expand 26!
%2826%2A25%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F21%21



Expand 21!
%2826%2A25%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29



%2826%2A25%2A24%2A23%2A22%2Across%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29%2F%28cross%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29 Cancel



26%2A25%2A24%2A23%2A22 Simplify




7893600 Now multiply 26*25*24*23*22 to get 7,893,600

So there are 7,893,600 possible passwords





2)

If order does matter, then the number of combinations is 8%21=8%2A7%2A6%2A5%2A4%2A3%2A2%2A1=40320

So there are 40,320 ways to rearrange the books




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 permutation formula:


n%21%2F%28n-r%29%21 Start with the permutation formula



10%21%2F%2810-7%29%21 Plug in n=10 and r=7



10%21%2F3%21 Subtract 10-7 to get 3



Expand 10!
%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F3%21



Expand 3!
%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%283%2A2%2A1%29



%2810%2A9%2A8%2A7%2A6%2A5%2A4%2Across%283%2A2%2A1%29%29%2F%28cross%283%2A2%2A1%29%29 Cancel



10%2A9%2A8%2A7%2A6%2A5%2A4 Simplify




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.