How many 3-digit numbers above 600 can be formed by using the digits 2, 3, 4, 5, 6, if repetition of digits is allowed?

Given: We have 5 digits i.e. 2,3,4,5,6


To Find: Number of 3-digit numbers


Condition: (i) Number should be greater than 600


(ii) Repetition of digits is allowed


For forming a 3 digit number, we have to fill 3 vacant spaces.


But as the number should be above 600, hence the first place must be occupied with 6 only because no other number is greater than 6.


Let us represent the 3-digit number


6



2,3,4,5,6



2,3,4,5,6



So the first place is filled with 6 = 1 ways


Second place can be filled with 5 numbers = 5 ways


Third place can be filled with 5 numbers = 5 ways


Total number of ways = 1 × 5 × 5 = 25


Total number of 3-digit numbers above 600 which can be formed by using the digits 2, 3, 4, 5, 6 with repetition allowed is 25


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