How many 3-digit numbers can be formed from the digits 1,2,3,4 and 5, assuming that:
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?
How many 3-digit numbers can be formed from the digits 1,2,3,4 and 5, assuming that:
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?
(i) The unit place can be filled by any one of the digits 1,2,3,4 and 5. So the unit place can be filled in 5 ways. Similarly the tens place and hundreds place can be filled in 5 ways each because repetition of digits is allowed.
∴ Total number of 3-digit numbers = 5×5×5=125
(ii) The unit place can be filled by any one of the digits 1,2,3,4 and 5. So the unit place can be filled in 5 ways. Now four digits are left. So the tens place can be filled in 4 ways. the hundreds place can be filled in 3 ways by the remaining 3 digits because repetition of digits is not allowed.
∴ Total number of 3-digit numbers = 3×4×5=60.
(i) The unit place can be filled by any one of the digits 1,2,3,4 and 5. So the unit place can be filled in 5 ways. Similarly the tens place and hundreds place can be filled in 5 ways each because repetition of digits is allowed.
∴ Total number of 3-digit numbers = 5×5×5=125
(ii) The unit place can be filled by any one of the digits 1,2,3,4 and 5. So the unit place can be filled in 5 ways. Now four digits are left. So the tens place can be filled in 4 ways. the hundreds place can be filled in 3 ways by the remaining 3 digits because repetition of digits is not allowed.
∴ Total number of 3-digit numbers = 3×4×5=60.
