SOLUTION: Permutations a) How many ways can 3 people be placed in one line where order is important? This is permutation. This is my first time using this site, could you also explain how

Question 856500: Permutations
a) How many ways can 3 people be placed in one line where order is important? This is permutation.
This is my first time using this site, could you also explain how you would figure this out on a graphics calculator (Texas Instruments TI-84 plus) i.e. what I would need to type in in order to get an answer (nPr?).
Thank you.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
3 people in a line and you want to figure out how many arrangements are possible .
that would be 3! which is equal to 3*2*1.
it is also equal to 3P3 which means choosing 3 people out of 3 where order is important.

in your ti-84 plus calculator, you would do the following for 3!:
press 3 then press math then press right arrow 3 times to PRB then enter 4 for ! then press enter.
you should get 6 because 3! is equal to 3*2*1 which is equal to 6.

in your ti-84 plus calculator, you would do the following for 3P3:
press 3 then press math then press right arrow 3 times to PRB then enter 2 for nPr then enter 3 then press enter.
you should get 6 because 3P3 is equal to 3*2*1 which is equal to 6.

3! and 3P3 will give you the same answer.
nPx is usually used for choosing x out of n where order is important.
x is usually smaller than n but doesn't have to be.
x can never be greater than n.

for example:
4P2 is equal to 4*3 which is equal to 12.

if order is not important, then use 4C2 which will be equal to (4*3)/2 = 6.

try these in your calculator.

in your ti-84 plus calculator, you would do the following for 4P2:
press 4 then press math then press right arrow 3 times to PRB then enter 2 for nPr then enter 2 then press enter.
you should get 12 because 4P2 is equal to 4*3 which is equal to 12.

in your ti-84 plus calculator, you would do the following for 4C2:
press 4 then press math then press right arrow 3 times to PRB then enter 3 for nCr then enter 2 then press enter.
you should get 6 because 4C2 is equal to (4*3)/(1*2) which is equal to 6.

the general formula for nPx is n! / (n-x)!

in practice, you can do the following:

assume 10P3

per the formula this is equal to 10! / (10-3)! which is equal to 10! / 7!

you carry the numerator down to 7! as shown below:

10P3 = (10*9*8*7!) / 7!

the 7! in the numerator and the 7! in the denominator cancel out and you are left with 10*9*8

notice that the multiplication is for 3 times which is the 3 in the 10P3.

so the shortcut for 10P3 is 10*9*8, because the 7! in the numerator and the 7! in the denominator will cancel out.

similarly, the formula for nCx is equal to n! / (n-x)! * x!)

you can do the same thing as follows:

assume 10C3.

this is equal to 10! / ((10-3)! * 3!) which is equal to 10! / (7!*3!)

you can rewrite this as (10*9*8*7!) / (7!*3!).

the 7! in the numerator and the 7! in the denominator cancel out and you are left with (10*9*8) / 3! which is equal to (10*9*8) / (1*2*3) which is easier to simplify and find what the number is.

so the shortcut for 10C3 is equal to (10*9*8)/3!.

of course, it's always simpler to use the calculator as shown above.
10P3 is equal to 720
10c3 is equal to 120

here's a reference from the web that you should find useful.
http://mathbits.com/MathBits/TISection/Algebra1/Probability.htm
at the bottom of that page is a link to the table of contents.
they will look like this:
http://mathbits.com/MathBits/TISection/Openpage.htm

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