Correct option (A) 192
Any number greater than 6000 but less than 10,000 that can be formed using the digits 3, 5, 6, 7 and 8 without repetition has its thousand place digit 6, 7 or 8.
Therefore, for the first left place, number of choices = 3
For second left place, number of choices = 4
For third left place, number of choices = 3
For fourth left place number of choices = 2
Therefore, the number of 4-digit numbers greater than 6000 = 72
Now, if we use all the 5 integers the number obtained is definitely greater than 6000; number of such numbers = 5! = 120
Therefore, total numbers formed = 72 + 120 = 192
