Question 856500
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.
<a href = "http://mathbits.com/MathBits/TISection/Algebra1/Probability.htm" target = "_blank">http://mathbits.com/MathBits/TISection/Algebra1/Probability.htm</a>
at the bottom of that page is a link to the table of contents.
they will look like this:
<a href = "http://mathbits.com/MathBits/TISection/Openpage.htm" target = "_blank">http://mathbits.com/MathBits/TISection/Openpage.htm</a>