Question:

If ${^{10}C_{x}} = {^{10}C_{x + 4}}$, find the value of x.

Updated On: Jul 6, 2022
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The Correct Option is C

Solution and Explanation

We have ${^{10}C_{x}} = {^{10}C_{x+4}}$ $\Rightarrow \, x + x + 4 = 10 \, \Rightarrow \, 2x = 6 \, \Rightarrow \, x = 3$
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Notes on permutations and combinations

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.