Question

Find the no of 3 digit numbers such that at least one of the digit is 6 (with repetitions)

Answer 1

We have to find Number of three digit numbers such that at least one of the digit is 6 (with repetitions).

There are total of 10 digits in all.

we can't keep 0 at hundred's place.

1. If all the three digits are 6 then total number of three digit number formed=1

2. If two of the digits are 6 , then total number of three digit number=66 (either of 9 digits) + 6 (either of 9 digits) 6+(either of 8 digits not zero)66

=9+9+8=26

3. If only one digit is 6 then total number of three digit number=1×9×9+8×1×9+8×9×1 where 1 means digit 6 if repetition of digits are allowed.

=81+72+72=225

So, total number of 3 digit numbers such that at least one of the digit is 6 (with repetitions)=1+ 26+225=252

Answer 2

Answer:

Step-by-step explanation:

We have to find Number of three digit numbers such that at least one of the digit is 6 (with repetitions).

There are total of 10 digits in all.

we can't keep 0 at hundred's place.

1. If all the three digits are 6 then total number of three digit number formed=1

2. If two of the digits are 6 , then total number of three digit number=66 (either of 9 digits) + 6 (either of 9 digits) 6+(either of 8 digits not zero)66

=9+9+8=26

3. If only one digit is 6 then total number of three digit number=1×9×9+8×1×9+8×9×1 where 1 means digit 6 if repetition of digits are allowed.

=81+72+72=225

So, total number of 3 digit numbers such that at least one of the digit is 6 (with repetitions)=1+ 26+225=252