Combinatorics



Combinatorics is a branch of applied Mathematics related to counting. Permutations and combinations are one of the major parts of Counting. Let us understand what permutations and combinations, in brief, are as follows.


Permutations

  • Suppose you need to arrange n group of people in r different places then the number of possible arrangements is given by permutations. For n > r, the permutations formula is given by,
  •  Arrangements are related to permutations and vice versa.
  • Order of the selection matters in permutations. That is, arrangement AB is different from arrangement BA.

Combinations

  • Suppose you need to choose r number of people from a group of n people then the number of possible selections is given by combinations. For n > r, the permutations formula is given by,
  • Selection is related to combinations and vice versa.
  • Order of the selection does not matter in combinations. That is, selection AB is exactly the same as selection BA.


Real-life situations

In our day-to-day life, we come across many counting problems as follows.

  1. Forming a committee of 5 people from a group of 10 men and 8 women.
  2. Arranging the class of 25 students on 40 benches.
  3. Choosing a car for serving from a group of 7 cars at a garage.
  4. Counting the number of possible Pizzas made of two toppings with different choices in two categories.


Refer to the examples based on Permutations and Combinations.