If $\, {{^n C}_{12}}$ =$\, {{^n C}_8}$ then $n$ is equal to
- 26
- 12
- 6
- 20
The Correct Option is D
Solution and Explanation
If ${ }^{n} C_{x}={ }^{n} C_{y}$, then
(i) $x=y$
(ii) $x + y = n $
$ \therefore { }^{n} C_{12}={ }^{n} C_{8} $
$ \Rightarrow n=12+8=20$
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.