If all the words with or without meaning made using all the letters of the word "KANPUR" a…

Question

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 440th position in this arrangement is :

Accepted Answer

Letters of KANPUR in alphabetical order: A, K, N, P, R, U --- all distinct, 6 letters, $6!=720$ total words.

Words starting with A: $5!=120$; with K: $120$ (total $240$); with N: $120$ (total $360$). Now within P-starting words ($361$ to $480$), position $440-360=80^{\text{th}}$ among P-words.

Within P-words, remaining letters A,K,N,R,U in order. Words starting PA: $4!=24$ (up to $384$); PK: $24$ (up to $408$); PN: $24$ (up to $432$); then PR-words start at position $433$. Position $440-432=8^{\text{th}}$ among PR-words with remaining letters A,K,N,U.

Words starting PRA: $3!=6$ (positions $433$--$438$); PRK: next, position $439$ is PRKANU, $440$ is PRKAUN.

$$\text{Answer: PRKAUN (Option B)}$$

Solutions · 1