Question

4. how many three digit numbers abc are formed where at least two of the three digits are same

Answer 1

We have to form a three digit number such that at least 2 of its digits are same.

We will solve it in reverse way i.e. firstly we will count all the numbers with distinct digits and then subtract it from the number of all possible three digit numbers.

Number of three digit numbers formed with all its digits distinct:—

First place can be filled with 9 ways, as 0 can not come here.

Second place can be filled with remaining 9 digits.

Third digit can be filled with remaining 8 digits.

Hence according to the principle of Multiplication:-

9∗9∗89∗9∗8

=648=648

Total number of 3 digits number formed = 9*10*10

= 900

Required number of digits = 900–648

=252=252

Hence the number of three digit numbers formed such that at least 2 of its digits are same are 252.