So the last few classes we have been learning about perms and coms.
Permulations- are the # of possible orderings of a set, provided that the order of set elements matters. Examples would be you phone digits..books on a shelf.locker combinations. Perms-BEST EXAMPLE EVER- put five blanks down on a sheet, then you put 26 (cause there is 26 letters in the alphabet)then 25 cause you used one then 24 then 23 then 22, and that equals: 7893 600 then the formula starts here: 26!/21!=n!/(n-r)!
n being the # of items to select from and r selecting items r at a time.
nPr=n!/(n-r)! "n things, permulated 5 at a time.
Coms- BEST EXAMPLE EVER: you have three different toppings for pizzas like turnips sardines and liver--> you have turnips + liver turnips+sardines sardines+liver, no matter what order you put them in its the same pizza ex) like turnips+liver, liver+turnips.
Perms: big #, order matters, nPr=n!/(n-r)!
Coms: small #, order does NOT MATTER, nCr=n!/(n-r)!
Another example: How many 3 digit #'s can be formed from digits 1,2,3,4,5,6,7
Provided they are both even+greater than 300? you then can make a ven diagram first circlwe having 3,5,7 middle circle having 4,6 then second circle having just 2. A=first # possible 3,4,5,6,7 B=even number ends in 2,4,6
Case 1= 5 time 5 times 1 = 25
Case 2= 4 times 5 times 1 =20
Case 3= 4 time 5 times 1 =20
All equal 65 3 digit even numbers greater then 300.

Another Example is Solve: nP2=30 n!/(n-2)! time (n-2)!/(n-2)!= three (and the (n-2) cancels out. n^2-n-30=0
(n+5)(9-6)=0 n=-5 n=6