Question

In how many ways can you arrange 6 digits to make a 3-digit number without repeating a digit?

Answer 1

The number of ways n different objects can be arranged, taking r objects at a time, without repeating any object is given by:

$^nP_r= \frac{n!}{(n-r)!}$

Given 6 different digits, the number of ways to arrange 6 different digits to make a 3 digit number without reapeating a digit is given by:

$^6P_3= \frac{6!}{(6-3)!} \\ \\ = \frac{6!}{3!} = \frac{6\times5\times4\times3!}{3!} \\ \\ =6\times5\times4=120$

Therefore, the number of ways 6 digits can be arranged to make a 3-digit number without repeating a digit is 120 ways.