Question

What is \[{}^n{C_r}\] in math?

Answer 1

Hint: The given question asks about \[{}^n{C_r}\] which part of combination is. In order to find out combination for a selection we use \[{}^n{C_r}\] .Therefore, in order to find out what \[{}^n{C_r}\] is, we will at first understand about permutations and combinations; then we will learn about \[{}^n{C_r}\] .

Complete step by step solution:
A permutation or combination is a group of items that are ordered. The "things" can be anything at all: a planet list, a number collection, or a list of groceries. You may have a list in a fixed order (such as 1st, 2nd, 3rd...) or a list that doesn't have to be in order (like the ingredients in a mixed salad).
Now, Let us know about combinations:
Any of the various selection groups that can be made at a time by taking any or all of a number of given items or objects is called a combination. The order of appearance of things is not taken into account in accordance with
Example: It is possible to create three classes of three separate items a, b, c, taking two at a time, i.e., ab, bc, ac.
Ab and Ba are the same party here. It is also obvious that the number of permutations (arrangements) is 2 for each combination (selection or group) of two items! For instance, there are two permutations for mixing ab, i.e., ab and ba.
In Mathematics, \[{}^n{P_r}\] and \[{}^n{C_r}\] are the functions of probability that describe permutations and combinations. The formula used to locate \[{}^n{P_r}\] and \[{}^n{C_r}\] is:
 \[{}^n{P_r} = \dfrac{{n!}}{{(n - r)!}}\] And \[{}^n{C_r} = \dfrac{{n!}}{{r!(n - r)!}}\]
Here's n.! It is the product of less than and equal to n for all positive integers.
Thus, \[{}^n{C_r} = \dfrac{{n!}}{{r!(n - r)!}}\]
Literal meaning of the above formula is, The method of selecting 'r' objects from a set of 'n' objects where the order of selection does not matter is in mathematics, combination or \[{}^n{C_r}\] .

Note: The one thing to make note here is that, Permutation is the way the elements of a group or a set are arranged in an order. Whereas, Combination is the choice of a group or a set of elements, where the order of the elements does not matter.