In how many ways can a teacher arrange 5 students in the front row of a classroom with a total of 40?
Since order matters this ia a permutation
40P5
I am going to finish the problem (my way) and then show you my fast method.
Pardon me if you already know it.
40P5=(40)(39)(38)(37)(36)=78960960
n= total number of objects you are choosing from
r= the number of objects you are choosing
................n!
nCr=*************
...........(n-r)!*r!
BUT I dont use it........to slow
Start with how I do a Permutation
10P2=..................start with 10 and count down 2 numbers
10P2=10*9...............2 numbers because of the 2 after the P
10P2=10*9=90
8P3=8*7*6=336
Now the Combination starts off the SAME way
10C2=10*9 EXCEPT now you have a denominator
......................to get the denominator you start with 1 and count up to 2
......................................... to whatever the number is following the C
.............10*9
10C2=*******=...............this how you set it up. Now either cancel or multiply
..............1*2
............10*9
10C2=******=90/2 =45
.............1*2
..........8*7*6
8C3=*******=.....cancel the 2*3 in the den. with the 6 in the num,.....=8*7=56
..........1*2*3
Special Note::::Only on combinations (not permutations) may you do the following
.............10*9*8*7*6*5*4
10C7=*******************.....NO, do not continue
.............1*2*3*4*5*6*7
Subtract......... 10 minus 7..........answer is 3
Replace the 7 with a 3
............10*9*8
10C3=********=10*3*4..(i reduced/canceled)..=120
.............1*2*3
