Question

What is the difference between ${}^n{P}_r$ and ${}^n{C}_r$ ?

Answer 1

Hint: Permutation ( ${}^n{P}_r$ ) can be defined as the different ways of arranging the elements of the group or a set in the specific desired order whereas the combinations ( ${}^n{C}_r$ ) can be defined as the selection of the elements from the group or a set where the specific order is not required and it does not matter.

Complete step by step solution:

Permutations	Combinations
Permutation can be defined as the arrangement of the items where the order of the items does matter and is important.	Combination can be defined as the selection of the items where the order of the items does not matter.
It gives the number of ways of the selection and the arrangement of the items in which order of the item is important.	It gives the number of ways of the selection of the items in which order of the items is not important and does not matter.
It is expressed as ${}^n{P}_r={\displaystyle \frac{n!}{(n-r)!}}$	It is expressed as ${}^n{C}_r={\displaystyle \frac{n!}{r!(n-r)!}}$
By using the single combination, many permutations can be derived.	By using one permutation, one combination can be derived.
Examples of permutations are arrangements of people, digits, numbers, alphabets, letters and the colors and many more.	Examples of combinations include the selection of menu, food, clothes, team members, employees and the study subjects.

Note: Always know the difference between both the given terms. Permutation is the arrangement of the items where order is important whereas the combination is the selection of the items where order is not important. Also remember the standard formulas for both the terms.