All the letters of the word "GTWENTY" are written in all possible ways with or without meaning, and these words are arranged as in a dictionary. The serial number of the word "GTWENTY" is:
All the letters of the word "GTWENTY" are written in all possible ways with or without meaning, and these words are arranged as in a dictionary. The serial number of the word "GTWENTY" is:
Solution and Explanation
Step 1: Calculate the Number of Words Starting with Each Letter
Words starting with \(E\): \(6! = 720 / 2 = 360\)
Words starting with \(G\) and second letter \(E\): \(5! = 120 / 2 = 60\)
Words starting with \(G\) and second letter \(N\): \(5! = 120 / 2 = 60\)
Words starting with \(GTE\): \(4! = 24\)
Words starting with \(GTN\): \(4! = 24\)
Words starting with \(GTT\): \(4! = 24\)
Step 2: Add the Serial Position of "GTWENTY"
"GTWENTY" itself contributes \(+1\).
Step 3: Total Serial Number of "GTWENTY"
\[ 360 + 60 + 60 + 24 + 24 + 24 + 1 = 553 \]
So, the correct answer is: 553
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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.