In this lesson we are going to learn about  special types of arrangements called "permutations." A permutation is an arrangement in which the order the items are arranged is important.
For example if we were to arrange the letters a,b and c......abc,cba,bac,bca,cab,acb would  be considered different permutations because in each arrangement the order is different.

_nP_r

The number of ways n things can be arranged in groups of size r
(and remember, order matters!)

nPr = n(n-1)(n-2)...
"r"  times

₅P₃= 5X4X3=60
r = 3, so we started at "5" and went down to "3".
 

 First we need to determine the "n" and the "r" in the problem. Since "n" is the number of things in our group, n = 4 (there are 4 books). And "r" is the number of items that will be in each arrangement. Since we are using all 4 books in each arrangement, r = 4 as well.
So plugging in our numbers for the "n" and the "r" we get this:

₄P₄ = 4 X 3 X 2 X 1 = 24
There are 24 different ways of placing those 4 books on a bookshelf.

    First determine the value of "n".....
that's right, it's 10! 
Next find the value of "r"......
right again, it's 3! 
Plug these values into the formula...

₁₀P₃  = 10 X 9 X 8 = 720 
WOW!!!  There are 720 different ways of arranging those 10 students into 3 person committees!!  

Since there are 11 players on the team, "n" = 11
And since each line-up has 5 players, "r" = 5
Plug in the values.....

₁₁P₅ = 11 X 10 X 9 X 8 X 7 = 55,440!!!
The coach has a choice of 55,440 different 5 player line-ups!!
And you thought coaching was easy!!!