First slide

Permutations

Question

If letters of the word $S A C H I N$ are arranged in all possible ways and are written out as in a dictionary, then the word $S A C H I N$ appears at serial number

Moderate

A

603
B

602
C

601
D

600

Solution

Letters appearing in the word SACHIN are A $, C, H, I, N, S$
The words beginning with letters $A, C, H, I$ and N appear before the word SACHIN.
There are $5 (5!) = 600$ words beginning with $A, C, H, I$ and $N$ .
Word $S A C H I N$ appears is the first word beginning with $S$ .
Therefore, $S A C H I N$ appears at serial number $601 .$

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