Question

How many numbers can be made with the help of the digits 0, 1, 2, 3, 4, 5 which are greater than 3000 (repetition is not allowed)

• A. 180
• B. 360
• C. 1380
• D. 1500

Answer 1

Answer: (C)

1380

Answer 2

All the 5 digit numbers and 6 digit numbers are greater than 3000. Therefore number of 5 digit numbers

= $6P_{5} -^{5} ⥂ P_{5} = 600$.

{Since the case that 0 will be at ten thousand place should be omit}. Similarly number of 6 digit numbers 6 ! – 5 ! = 600.

Now the numbers of 4 digit numbers which are greater than 3000, having 3, 4 or 5 at first place, this can be done in 3 ways and remaining 3 digit may be filled from remaining 5 digits i.e., required number of 4 digit numbers are

$5P_{3} \times 3 = 180$.

Hence total required number of numbers = 600 + 600 + 180 = 1380.