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Chapter 5: Problem 428

If the letters of the word SACHIN are arranged in all possible ways and these words are written in dictionary order then the word SACHIN appears at serial number (a) 600 (b) 601 (c) 602 (d) 603

Short Answer

Expert verified
The word SACHIN appears at serial number 601 in the dictionary, considering all possible arrangements of its letters in alphabetical order. The correct answer is (b) 601.

Step by step solution

01

Calculate the total number of arrangements for the letters A, C, H, I, N, and S

Since there are 6 letters in the word SACHIN, there are 6! possible arrangements, where n! (factorial) is the product of all positive integers less than or equal to n: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 So, there are 720 possible arrangements of the letters in the word SACHIN.
02

Determine the position of each letter in alphabetical order

To find the position of the word SACHIN, we will first find the order of each letter in alphabetical order: A - 1 C - 2 H - 3 I - 4 N - 5 S - 6
03

Start with the first letter S and count the arrangements that come before SACHIN

In dictionary order, we will first arrange words with A, C, H, I, and N as their first letters, followed by words with S as their first letter. So, the words starting with each of the first 5 letters will have 5! arrangements each: 5! × 5 = 120 × 5 = 600 This means that 600 words come before any words that start with S.
04

Consider the arrangements starting with S

Finally, we need to include words starting with S. The word SACHIN would be the first one in lexicographical order among all the words starting with S: S (followed by words arranged in alphabetical order: A, C, H, I, and N) So, we only need to add 1 to the previous count of 600 words: 600 + 1 = 601
05

Choose the correct answer

According to our calculations, the word SACHIN appears at serial number 601 in the dictionary. So, the correct answer is: (b) 601

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