Permutation and Combination # 2

2. If the letters of the word SACHIN are arranged in all possible ways and these
Words are written out as in dictionary, then the word ‘SACHIN’ appears at serial
Number?
( a ) 601 ( b ) 600 ( c ) 603 ( d ) 602

Ans: a)
Solutions: if the word started with the letter A then the remaining 5 positions can be filled in `
5! Ways
If it started with c then the remaining 5 positions can be filled in 5! Ways
Similarly if it started with H,I,N the remaining 5 positions can be filled in 5! Ways.
If it started with S then the remaining position can be filled with A,C,H,I,N in
alphabetical order as on dictionary
The required word SACHIN can be obtained after the 5X5!=600 Ways
i.e. SACHIN is the 601th letter