Question:

If all permutations of the letters of the word are arranged in the order as in a dictionary, what is the $49^{th}$ word?

Updated On: Jul 6, 2022
  • AAGIN
  • NAAGI
  • IAAGN
  • GAAIN
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The Correct Option is B

Solution and Explanation

Starting with letter $A$, and arranging the other four letters, there are $4! = 24$ words. These are the first $24$ words. Then starting with $G$, and arranging $A, A, I$ and $N$ in different ways, there are $\frac{4!}{2!1!1!} = 12$ words. Next the $37^{th}$ word starts with $I$. There are again $12$ words starting with $I$. This accounts up to the $48^{th}$ word. The $49^{th}$ word is $NAAGI$.
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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.