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= (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= (6!)/((6-3)!) \\ \\ = (6!)/(3!) = (6*5*4*3!)/(3!) \\ \\ =6*5*4=120`

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