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

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288

310

360

306

answer is C.

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Detailed Solution

Using the digits 0, 1, 2, 3, 4, 5 greater than 4321

Case I : No of 4 digit numbers starting with 5 = 1x6x6=6³

0 to 5

Case II : No of 4 digit numbers fixing 4, 3, 2 in first 3 places.

2, 3, 4, 5

Units place can be filled with 2, 3, 4, 5 = 4

Case III : No of 4 digit numbers begin with 43

4, 5

0 to 5

Third place can be filled using 3, 4, 5 in 3 ways.

Units place can be filled using 0 to 5 in 6 ways.

No. of permutations=3(6)

Case IV :

4 or 5

0 to 5

Numbers starting with 4.

Second place can be filled using 4, 5. Last 2 places using 0 to 5 in 6 ways

$∴$ No of permutations=2(6) (6)=72

Total=216+4+18+72=310

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