How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated ?

Three digit number will have unit?s, ten?s and hundred?s place.

Out of 5 given digits any one can take the unit?s place.

This can be done in 5 ways. ...              (i)

After filling the unit?s place, any of the four remaining digits can take the ten?s place.

This can be done in 4 ways. ...              (ii)

After filling in ten?s place, hundred?s place can be filled from any of the three remaining digits.

This can be done in 3 ways. ... (iii) 

So,by counting principle, the number of 3 digit numbers = 5x 4 x 3 = 60