Question

All the six letters of the name SACHIN are arranged to form different words without repeating any letter in any word. The words so formed are then arranged as in the dictionary. What will be the position of the word SACHIN in that sequence?
A) 436
B) 590
C) 601
D) 751

Answer 1

Hint:
Use the method of combinations and some general knowledge that how the words are arranged in a dictionary. We know that, if we have to find “study” meaning in dictionaries then first we’ll reach to the page of “s” then we’ll find the page of “st” then “stu” then “stud” and in the end “study”. On this page, we’ll get the meaning of study.

Complete step by step solution:
The word given to us is SACHIN.
Now we have to form all the words that we can from these letters but without repeating the letter is the condition.
So we will take the letter as they occur in the dictionary itself. That is A, C, H, I, N and then S.
A number of words formed from letter A are \[5! = 120\]
Because letter A is fixed and the remaining 4 letters will form the word.
Similarly for letter C, H, I, N will form 120 words each.
Now total words so formed are = \[120 + 120 + 120 + 120 + 120 = 600\]
Now it comes to letter S. It will also form 120 words with a combination of remaining letters.
But we have to arrange them according to the dictionary.
On observing we will come to know SACHIN is the first word after arranging the
words of letter S (because all letters are already in dictionary pattern)
Thus it ranks 601 in the list.

So, option C is the correct answer.

Note:
Many students make mistakes in counting. There is a tool in math to count the number of chosen numbers in a specific pattern. there are permutations and combinations. Whenever we have to do any arrangement, we use permutation and when we have to choose n items out of r we choose combinations.