Question:
The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is
The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is
Updated On: Mar 20, 2025
- 79
- 86
- 84
- 89
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The Correct Option is D
Solution and Explanation
(A)Arrange the letters of OUGHT in alphabetical order: G, H, O, T, U.
(B) Count words starting with each letter before ""T"":
\[
G \to 4!, \quad H \to 4!, \quad O \to 4!.
\]
(C) Count words starting with ""T"" but second letter as:
\[
TG \to 3!, \quad TH \to 3!, \quad TOG \to 2!, \quad TOH \to 2!.
\]
(D) Add the counts:
\[
4! + 4! + 4! + 3! + 3! + 2! + 2! + 1! = 89.
\]
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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.