Three digit number

hey_thr67 wrote:How many different three-digit numbers contain both the digit 2 and the digit 6?

In 3 places, we have to place 2, 6, and a third digit from 0 to 9.
Now, for placing 2 we have 3 positions. After placing 2, we have 2 positions left for 6. And after placing 6, we are left with one position to place any of the 10 digits.

Hence, number of integers = 3*2*10 = 60

Now, within these 60 integers there are 026 and 062, which are not three-digit integers. Also we are double counting the following integers 226, 262, 266, 622, 626, and 662, i.e. 6 integers.

Hence, total number of different three-digit numbers contain both the digit 2 and the digit 6 is (60 - 2 - 6) = 52

The correct answer is A.