Question:

 If  nC8 = nC2, find nC2.

Updated On: Oct 21, 2023
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Solution and Explanation

It is known that,\(^nC_a= \space^nC_b\)
\(⇒a=b\space or\space  n=a+b\)
Therefore\(,^nC_8\space =\space ^nC_2\)
\(⇒n=8+2=10\)
\(∴ ^nC_2=\space^{10}C_2=\frac{10}{2!\left(10-2\right)!}\)
\(=\frac{10!}{2!8!}=\frac{10\times9\times8!}{2\times1\times8!}=45\)

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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.