Question

What is the corresponding rank of the word RACHIT?

Answer 1

Hint: In this question, the letters of the word “RACHIT” to be arranged in the alphabetical order and the position needed to be determined for which we need to use the concept of combination by evaluating the number of words formed by keeping every letter at consequent positions.

Complete step-by-step answer:
The letters of the word “RACHIT” are arranged in alphabetical order as ACHIRT

The number of words starting with the letter “A” can be calculated $ 5! $ .
Similarly,
The number of words starting with the letter “C” can be calculated as $ 5! $ .
Again,
The number of words starting with the letter “H” can be calculated as $ 5! $ .
Again,
The number of words starting with the letter “I” can be calculated as $ 5! $ .

Now for the letter R, since the letter R is the first letter in the word “RACHIT”, so we will fix the letter R in the first position hence by further arranging the letters in ascending order we can write
\[\Rightarrow R \underline A \underline C \underline H \underline I \underline T \]
So the rank of the letter RACHIT where R is fixed at the first position, we get
\[
\Rightarrow RACHIT = 4 \times 5! + 1 \\
   = 4 \times 5 \times 4 \times 3 \times 2 \times 1 + 1 \\
   = 480 + 1 \\
   = 481 \\
 \]
Hence the rank of the word RACHIT will be \[ = 481\]

Note: Combination is the number of ways in which definite objects/letters can be arranged in a defined manner. Candidates should be aware while using the ascending order of the alphabets and while using the formula of combinations.