How many 3-digit number can the formed by using the digit $1,2,3,4,5,6,7,8$ if no digit is repeated?

We have to select $3$ numbers from the $8$ numbers ${(}^8{C}_3)$ and permute them over the three places.

$\Rightarrow$ ways $={}^8{C}_3\times 3!=\frac{8!}{3!5!}\times 3!$

$=8\times 7\times 6=8\times 42=336$.