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Solution


Q.

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                      [2023]
1 580    
2 582   
3 576   
4 578  

Ans.

(2)

No. of words formed when word starts from B = 5!

No. of words formed when word starts from C = 5!

No. of words formed when word starts from I = 5!

No. of words formed when word starts from L = 5!

No. of words formed when word starts from PB = 4!

No. of words formed when word starts from PC = 4!

No. of words formed when word starts from PI = 4!

No. of words formed when word starts from PL = 4!

No. of words formed when word starts from PUBC = 2!

No. of words formed when word starts from PUBI = 2!

No. of words formed when word starts from PUBLC = 1

Now, the word comes is PUBLIC = 1

∴ Serial number of word PUBLIC

= 4 × 5! + 4 × 4! + 2 × 2! + 1 + 1 = 582