A small combination lock on a suitcase has 3 wheels, each labeled with the 10 digits 0 to 9. How many 3 digit combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different?

a) The number of different 3 digit combinations possible if no digit is repeated is…..?

b) The number of different 3 digit combinations possible if digits can be repeated is …..?

c) The number of different 3 digit combinations possible if successive digits must be different is …..?

*Solution:-*

a) 10*9*8 = 720

b) 10*10*10=1000

c) 10*9*9= 810

How did you get the answer for C using the counting principle?