How many six digit numbers greater than 700 000 can be made from the digits 2, 2, 4, 4, 4, 7?

Question

A. 10
B. 60
C. 64
D. 120

Answer 1

If it has to be greater than 700000, the first digit must be 7. That leaves us with 5 digits 2,2,2,4,4 to make the remainder of the number.

Here we have 5 digits of which 2 and 3 are identical, so the number of ways to choose the 5 digits is
C(5,3,2) = 5!/(3!2!)
I'll let you do the rest.