Question:

Four writers must write a book containing $17$ chapters. The first and third writer must write $5$ chapters each, the second writer must write $4$ chapters and fourth writer must write three chapters. The number of ways that can be found to divide the book between four writers, is

Updated On: Jul 6, 2022
  • $\frac{17!}{\left(5!\right)^{2} 4! 3! 2!}$
  • $\frac{17!}{5! 4! 3! 2!}$
  • $\frac{17!}{\left(5!\right)^{2} 4! 3! }$
  • $\frac{17!}{\left(5! \right)^{2}\times4 \times 3}$
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The Correct Option is C

Solution and Explanation

Evidently $(c)$ is correct option because we have to divide $17$ into four groups each distinguishable into groups of $5$, $5$, $4$ and $3$
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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.