Question

What do ${}^{n}P_r$ and ${}^{n}C_r$ mean?

Answer 1

The meaning of ${}^{n}P_r$

• The permutation is the arrangement of elements in a definite order.
• The $P$in the term ${}^{n}P_r$ denotes permutation.
• The ${}^{n}P_r$formula gives the number of ways of arranging $r$elements from a set of $n$ elements.

${}^{n}P_r=\frac{n!}{\left(n-r\right)!}$, where $n$ is the total number of elements and $r$is the number of elements that have to be arranged.

The meaning of ${}^{n}C_r$

• The combination is the selection of elements from a given set of elements. The order of selection does not matter.
• The $C$in the term ${}^{n}C_r$ denotes combination.
• The ${}^{n}C_r$formula gives the number of ways of selecting $r$elements from a set of $n$ elements where the order does not matter.

${}^{n}C_r=\frac{n!}{r!\left(n-r\right)!}$, where $n$ is the total number of elements and $r$is the number of elements that have to be selected.