About NCR Formula
Let us first define NCR before learning the NCR formula. NCR is a combination and an arrangement where the order of the objects is irrelevant. NCR is defined as the selecting of items without regard for the arrangement's order. The NCR formula is used to determine all feasible configurations where the order is not taken into account.
The NCR formula is used to calculate the number of ways in which r objects are picked from n objects in any order. The following is a representation of it.
Derivation of NCR Formula
P(n,r), the number of ways to permute r elements from a total of n, can be calculated as follows:
- Using any of the C(n,r) methods to create a combination of r components from a total of n.
- These r elements can be arranged in any of r! ways. The number of ways to make permutations is determined by the multiplication principle.
is P(n,r)= C(n,r)×r!
Using the permutations formula P(n,r)=n!/(n-r)! to substitute in the formula above:
n!/(n−r)!=C(n,r)r!
As a result of resolving this, the number of combinations, C(n,r)=n!/[r!(n−r)!]
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