Answer:
Permutations formula [tex]P(n,k)=\dfrac{n!}{(n-k)!}[/tex].
Combinations formula [tex]C(n,k)=\dfrac{n!}{k!(n-k)!}[/tex]
Step-by-step explanation:
The premutations formula gives us the number of ways that we can choose k elements of a set of n elements, taking into account the order in which we choose the elements and is given by
[tex]P(n,k)=\dfrac{n!}{(n-k)!}[/tex]
The formula for combinations gives us the numbers of ways that we can choose k elements of a set of n elements without taking into account the order of the object. It's is given by
[tex]C(n,k)=\dfrac{n!}{k!(n-k)!}[/tex]
Ex: Let us take the set of letters [tex]\mathbf{L}=\{A \quad B \quad C \quad D\}[/tex]
- C(4,2) gives us the number of pairs of letters that we can form with the letters from the set [tex]\mathbf{L}[/tex], in this case we the pairs AB and BA are the same.
-P(4,2) gives us the number of pairs of letters that we can form with the letters from the ser [tex]\mathbf{L}[/tex] taking into acount the order of the pair, in this case the pairs AB and BA are different.
