3.24: Even 5-digit numbers greater than 50 000

A 5-digit number is made using the digits 0, 1, 4, 5, 6, 7 and 9. No digit may be used more than once. Find how many such 5-digit numbers are even and greater than 50 000.

The number of combinations of $n$ objects taken 4 at a time is equal to 6 times the number of combinations of $n$ objects taken 2 at a time. Calculate the value of $n$.