rakeshd347 wrote:How many odd three-digit integers greater than 800 are there such that all their digits are different?
A. 40
B. 60
C. 72
D. 81
E. 104
We need to determine how many integers greater than 800 but less than 1,000 are odd and contain different digits.
Let's start with the numbers from 801 to 899, inclusive.
There is
1 option for the hundreds digit ( the digit of 8),
5 options for the units digit (digits of 1, 3, 5, 7, or 9), and
8 options for the tens digit (since we cannot use the number used in the hundreds or units place. Thus, between 800 and 900, there are 1 x 5 x 8 = 40 possibilities.
Next, let us consider numbers from 901 to 999, inclusive.
There is
1 option for the hundreds digit ( the digit of 9),
4 options for the units digit (digits of 1, 3, 5, or 7), and
8 options for the tens digit (since we cannot use the number used in the hundreds or units place. Thus, between 900 and 1000, there are 1 x 4 x 8 = 32 possibilities.
So, in total, there are 40 + 32 = 72 possibilities.
Answer:
C
