Question ID: #561
If all the words with or without meaning made using all the letters of the word “KANPUR” are arranged as in a dictionary, then the word at $440^{th}$ position in this arrangement, is:
- (1) PRNAKU
- (2) PRKANU
- (3) PRKAUN
- (4) PRNAUK
Solution:
The letters of the word “KANPUR” in alphabetical order are: A, K, N, P, R, U.
We need to find the word at the $440^{th}$ position.
Words starting with A: $5! = 120$
Words starting with K: $5! = 120$
Words starting with N: $5! = 120$
Total words so far = $120 + 120 + 120 = 360$.
We need to reach 440, so the $440^{th}$ word must start with P.
Words starting with PA: $4! = 24$. (Cumulative Total = $360 + 24 = 384$)
Words starting with PK: $4! = 24$. (Cumulative Total = $384 + 24 = 408$)
Words starting with PN: $4! = 24$. (Cumulative Total = $408 + 24 = 432$)
The next letters in alphabetical order after N is R. So, we check words starting with PR.
Words starting with PRA: $3! = 6$. (Cumulative Total = $432 + 6 = 438$)
We are now very close to 440. The next word starts with PRK. The remaining letters are A, N, U.
$439^{th}$ word: P R K A N U (Alphabetical order of remaining letters)
$440^{th}$ word: P R K A U N
Ans. (3)
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