All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is

Question

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is, 576, 578, 580, 582

MARKS App · Accepted Answer

The given word is PUBLIC Arranging the letters alphabetically, we get BCILPU When the word starts with any of the letters B/C/I/L, the number of possibilities = 5 ! × 4 = 480 Now when the word starts with PB, then the number of possibilities = 4 ! = 24 Now when the word starts with PC, then the number of possibilities = 4 ! = 24 Now when the word starts with PI, then the number of possibilities = 4 ! = 24 Now when the word starts with PL, then the number of possibilities = 4 ! = 24 Now when the word starts with PUBC, then the number of possibilities = 2 ! = 2 Now when the word starts with PUBI, then the number of possibilities = 2 ! = 2 Now when the word starts with PUBLC, then the number of possibilities = 1 Now when the word starts with PUBLIC, then the number of possibilities = 1 Rank = 480 + 24 × 4 + 2 × 2 + 1 × 2 = 582 Hence, rank of the work PUBLIC is 582 .

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