Number of words made from AGAIN = \(\frac{5!}{2!}\)
= 60
To get the number of words starting with , we fix the letter at the extreme left position, we then rearrange the remaining 4 letters taken all at a time. There will be as many arrangements of these 4 letters taken 4 at a time as there are permutations of 4 different things taken 4 at a time.
Hence, the number of words starting with = 4!
= 24
Then, starting with , the number of words = \(\frac{4!}{2!}\) = 12
As after placing at the extreme left position, we are left with the letters , and . Similarly, there are 12 words starting with the next letter .
Total number of words so far obtained = 24 + 12 + 12+ = 48
The 49th word is NAAGI. The 50th word is NAAIG.
