Question:

If $ ^{2n+3}C_{2n} - \,^{2n+2}C_{2n-1} = 15 \left(2n+1\right)$, then $n= $

Updated On: Sep 25, 2024
  • $13$
  • $14$
  • $27$
  • $15$
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The Correct Option is B

Solution and Explanation

$\frac{\lfloor2n+3 }{\lfloor2n \lfloor3} -\frac{ \lfloor2n+2}{\lfloor2n-1\lfloor3} = 15\left(2n+1\right) $ $ \Rightarrow \frac{\left(2n+2\right)\left(2n+1\right)}{2} = 15\left(2n+1\right) $ $ \Rightarrow n+1=15$ $\Rightarrow n=14.$
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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.