Question

How many 4-digit numbers which are greater than 5000can be formed using the digits 7,0,5and 4?

Answer 1

Since the numbers have to be greater than 5000, we have to choose either 5 or 7 as first digit.

If we choose 5, we can arrange the remaining 3 digits in 3!=6 ways:

5047, 5074, 5704, 5740, 5407, 5470

All these numbers are something like "five thousand and something", so they are greater than 5000.

Similarly, if we choose 7, we can arrange the remaining 3 digits in 3!=6 ways:

7045, 7054, 7504, 7540, 7405, 7450

All these numbers are something like "seven thousand and something", so they are greater than 5000.