The number of four-digit numbers strictly greater

Question:

The number of four-digit numbers strictly greater than 4321 that can be formed using the digits $0,1,2,3,4,5$ (repetition of digits is allowed) is :

  1. 288

  2. 306

  3. 360

  4. 310


Correct Option: , 4

Solution:

(1) The number of four-digit numbers Starting with 5 is equal to $6^{3}=216$

(2) Starting with 44 and 55 is equal to $36 \times 2=72$

(3) Starting with 433,434 and 435 is equal to $6 \times 3=18$

(3) Remaining numbers are $4322,4323,4324,4325$ is equal to 4 so total numbers are

$216+72+18+4=310$

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