Correct Answer - Option 1 : 69
Given:
To find the rank of the word OTHER
The concept used:
Finding Rank of a word in Permutations and Combinations
Formula used:
n! = n × (n - 1) × (n - 2) × (n - 3) × (n - 4) ... × 1
Calculation:
Arrange all the alphabets in alphabetical order like (E, H, O, R, and T)
Now in the dictionary words will appear in alphabetical order, so the first words will appear starting alphabet “E“.
When "E" is fixed at the first position, the rest 4 alphabets can be arranged in 4! = 24 ways.
The next starting alphabet will be “H” and again there will be 4! = 24 words starting with “M“.
Next will be starting with “O“, and next alphabet as “E” we’ll have 3! = 6 words.
Next will be starting with “O“, and next alphabet as “H” we’ll have 3! = 6 words.
Similarly, starting with “O“, and the next alphabet as “R” we’ll have 3! = 6 words.
Next will be starting with “O“, and next alphabet as “T” and next as “E” we’ll have 2! = 2 words
Next will be starting with “O“, and next alphabet as “T” and next as “H” will have 2! = 2 words but the first word will be 0 > T > H > E > R which is the desired word.
So the rank of word OTHER in the dictionary will be
⇒ 4! + 4! + 3! + 3! +3! + 2! + 1
⇒ 69
∴ The word OTHER will be at the 69th position if we form the whole words that can be created using the letters of OTHER arranged in dictionary order.
