JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Permutations and Combinations

Arranged alphabetically the letters are B, C, I, L, P, U. Counting the words preceding PUBLIC: words beginning with B, C, I or L number $4\times 5!=480$. Among words beginning with P, the second letter U is preceded by B, C, I, L, contributing $4\times 4!=96$. With PU fixed, the third letter B has no earlier letter. With PUB fixed, the fourth letter L is preceded by C and I, contributing $2\times 2!=4$. With PUBL fixed, the fifth letter I is preceded by C, contributing $1\times 1!=1$. The number of preceding words is $480+96+4+1=581$, so the serial number of PUBLIC is $582$.