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:

• A. 580
• B. 578
• C. 576
• D. 582

Answer 1

The Correct Option is D

The total number of permutations of the letters of the word PUBLIC is \(6! = 720\). We break the calculation down step by step: \[ B\_\_\_\_\_\_\_\_ = 5! = 120 \] \[ C\_\_\_\_\_\_\_\_ = 5! = 120 \] \[ I\_\_\_\_\_\_\_\_ = 5! = 120 \] \[ L\_\_\_\_\_\_\_\_ = 5! = 120 \] \[ PB\_\_\_\_\_\_\_ = 4! = 24 \] \[ PC\_\_\_\_\_\_\_ = 4! = 24 \] \[ PI\_\_\_\_\_\_\_ = 4! = 24 \] \[ PL\_\_\_\_\_\_\_ = 4! = 24 \] \[ PUBC\_\_\_\_\_ = 2! = 2 \] \[ PUBI\_\_\_\_\_ = 2! = 2 \] \[ PUBLIC\_\_\_\_ = 1 \] Thus, the rank of PUBLIC is 582.