Question

Words are made with or without meaning from letters of the word AGAIN. If these words are written as in a dictionary , what is the ${55}^{th}$ word?

• A. GIANA
• B. INAAG
• C. NGAAI
• D. ANAGI

Answer 1

The correct option is C

NGAAI

There are 5 letters in the word AGAIN in which A appears twice.
So, number of words possible = 60
Letters of the given word in alphabetical order is A A G I N
Let us proceed in trial and error manner.
Number of words with A as first letter:
A _ _ _ _
The 4 places can be filled with 4 remaining letters A G I N in 4! ways = 24 words
In the dictionary order, the words that follow start with G.
G _ _ _ _ $\to$Number of words = 12 ( As there are 2 A's involved)
Now, number of all the words made till now = 24+12 = 36 ( < 55)
Next words begin with I
I _ _ _ _ $\to$Number of words = 12
Now, number of all the words made till now = 36+12 =48
As all the remaining words start with N, we start filling $2^{nd}$ place
NA _ _ _ $\to$Number of words = 6
Number of words till now = 48+6 = 54