AIEEE 2005 (Offline)Question 1
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
Permutation and Combination
Solution
Concept. Count words starting with letters before S, then SACHIN is the first S-word. Formulas used. (1) Words with a fixed first letter: $5!$Step 1 - Order. A, C, H, I, N, S. Step 2 - First letter A, C, H, I or N. $5\cdot5!=600$. Step 3 - S-words. The rest A, C, H, I, N already in alphabetical order: SACHIN is the first. Step 4 - Rank. $600+1=601$. Answer: A