How many numbers between $3000$ and $4000$ can be formed from the digits $3,4,5,6,7$ and $8$ with no digits being repeated in any number?

The correct option is B $60$
The first place filled with $3-1$ way
Second place $-5$ways
Third place $-4$ ways
Fourth place $-3$ ways
Total numbers $=1\times 5\times 4\times 3=60$ ways
Hence, option 'C' is correct.