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)?

$180$

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$360$

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$1380$

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$1500$

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Solution

The correct option is C
$1380$

Explanation for the correct option:
The total numbers can be formed.
We have total $6$ digits here which are $0, 1, 2, 3, 4, 5$ .
We have formed numbers that are greater than $3000$ we can write, $4$ -digit numbers, $5$ digit numbers and $6$ digit numbers.
Thus,
Four-digit numbers $= 3 x 5 x 4 x 3 = 180$
Five-digit numbers $= 5 x 5 x 4 x 3 x 2 = 600$
Six-digit numbers $= 5 x 5 x 4 x 3 x 2 x 1 = 600$
Therefore the total numbers formed $= 180 + 600 + 600 = 1380$
Hence the correct option is C.

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Similar questions

How many four digit different numbers, greater than 5000 can be formed with the digits 1,2,5,9,0 when repetition of digits is not allowed?

How many 5 digit even numbers can be made from the digits 0,1,2,3,4,5 if repetition is not allowed?

3, 4, 5, 6, 7, 8

3000

4000

5

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