How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0

Question:

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?

Solution:

As the number has to be greater than 5000, the first digit can either be 5 or 9.

Hence, it can be filled only in two ways.

Number of ways for filling the second digit = 4

Number of ways for filling the third digit = 3           (as repetition is not allowed)

Number of ways for filling the fourth digit = 2

Total numbers $=2 \times 4 \times 3 \times 2=48$

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