Permutations & Combinations

[Wildiris]

Can someone please explain to me how permutations work. Specifically, how many different license plates or phone numbers are possible with a with a five digit license plate or seven digit phone number. It seems to me that there is a simple formula, but I'm somehow unable to wrap my mind around at this moment.

 

Thanks for the help,

Wildiris

[coffeegal]

Multiplication. For a 5 number license plate it is: 10*10*10*10*10 because you have 10 different possiblities (0-9) for each of the 5 places. If, on the other hand, you are not allowed to re-use any digit, the answer would be: 10*9*8*7*6. :D

[WTMindy]

This is a more in depth answer to your question than Coffeegal gave, although she was exactly right for the problem you mentioned.

 

You use the permutation formula when order matters. (For example, XYZ is a different licence plate than YZX, so the order of the letters matters). The formula is nPk = n!/(n-k)! N is the number of items in the group and k is how many you are choosing. The exclamation mark means factoral. 4! = 4*3*2*1

 

you use combinations when order doesn't matter (For example: choose a committee of 3 students out of 10 total students. Johnny, Sally, and Sam is the same committee as Sally, Johnny and Sam.) The formula is

 

nCk = n!/k!(n-k)!

 

Here is a website that expains it in more depth. Maybe this was more than you wanted!! :-)

 

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