How many numbers greater than 1200 can be formed with the digits 3, 4, 5, 6, 7 and 8 if a digit cannot occur more than once in a number?

To find the number of numbers  greater than 1200 that can be
formed with 6 digits 3, 4,5,6 and 8 without repetition:

We see that
all the digits 3,4,5, 6 and 8 are greater than the digits 1 and
2.

Therefore any 4 digit  numbers formed  with the given digits are 
greater than 1200. Also any 5 and 6 digit numbers formed are geater than 1200. Also there is a
condition of no repetetion.

The number of 4 digit numbers with the
given 6 digits without repetion is 6P4 = 6*5*4*3 = 360.

The the
number of 5 digit numbers  that can be formed without repetition with 6 given digits = 6*5*4*3*2
= 720 ways.

The number ways the 6 digit numbers using all the 6
digits without repetitions = 6! = 6*5*4*3*2*1 = 4320.

Therefore the
number of numbers formed using the given six digits without repetition is  6P4+6P5 +6P6  =
360+720+ 720 =  1800.