Question

All the words that can be formed using alphabets A, H, L, U, R are written as in a dictionary and no alphabet is repeated. What will be the rank of word RAHUL?
A \[71\]
B \[72\]
C \[73\]
D \[74\]

Answer 1

Hint: Permutation is the arrangement of items in some particular sequence. In this question there are five alphabets and need to form words without repeating the alphabets. In the dictionary words are always in alphabetical order. First find all the words that start with each given alphabet. Then check the word that starts with the alphabet R. Then find the rank of the word RAHUL.

Formula Used: \[n! = 1 \times 2 \times 3 \times ... \times n\]
Here, n is natural number.

Complete step by step solution: There are five alphabets A, H, L, U and R. The alphabetical order of the given alphabets is A, H, L, R and U.
Now, calculate number of words starting with alphabet A.
\[\begin{array}{l}4! = 1 \times 2 \times 3 \times 4\\4! = 24\end{array}\]
Calculate number of words starting with alphabet H.
\[\begin{array}{l}4! = 1 \times 2 \times 3 \times 4\\4! = 24\end{array}\]
Now, calculate number of words starting with alphabet L.
\[\begin{array}{l}4! = 1 \times 2 \times 3 \times 4\\4! = 24\end{array}\]
Hence, calculate total numbers words before words starting with R.
Total numbers words before words starting with R \[24 + 24 + 24 = 72\]
The first words starting with R is RAHLU and the second word is RAHUL. Hence, the word RAHLU is at rank 73 and the word RAHUL is at 74.
So, the word RAHUL has Rank 74.

Option ‘D’ is correct

Note: The common mistake happen here by students are taking permutation of all alphabets which is wrong.