Respuesta :
We have been given two expressions [tex]9P9\text{ and }9C9[/tex]. We are asked to find the value of each.
To find 9P9, we will use permutations formula.
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex], where
P = Number of permutations,
n = The total number of objects in the set,
r = Number of objects being chosen from the set.
[tex]9P9=\frac{9!}{(9-9)!}[/tex]
[tex]9P9=\frac{9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{(0)!}[/tex]
[tex]9P9=\frac{362880}{1}[/tex] Using [tex]0!=1[/tex]
[tex]9P9=362880[/tex]
To find 9C9, we will use combinations formula.
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex], where
C = Number of combinations,
n = The total number of objects in the set,
r = Number of objects being chosen from the set.
[tex]9C9=\frac{9!}{9!(9-9)!}[/tex]
[tex]9C9=\frac{9!}{9!(0)!}[/tex]
[tex]9C9=\frac{9!}{9!\cdot 1}[/tex] Using [tex]0!=1[/tex]
Cancelling out [tex]9![/tex], we will get:
[tex]9C9=\frac{1}{1}[/tex]
[tex]9C9=1[/tex]
The answers differ because order. With permutations we care about the order of the elements, while with combinations we don't.
