Odd 3-digit numbers

lali_mew wrote:This could be a repeat. I couldnt dig up an older matching topic though.

How many odd 3-digit integers greater than 800 are there such that their digits are different?
A)40
B)56
C)72
D)81
E)104

OA - [spoiler]C)72[/spoiler]

I could find the answer by actually browsing through the 100 odd numbers between 801 and 999 included. I'm sure there's a shorter way. Can anyone help me with this?

Here is the process:

for first digit we have 2 options (8,9)
for second digit we have 9 options (1,2,3,4,5,6,7,8,9,0)=10-1(which is used in the first option) = 9
for third digit we have 5 options (1,3,5,7,9).

we have to place 1 at the third digit.
2*8*1 = 16
first place can be arranged in two ways (8,9)
third place can be arranged in one way (1)
second place can be arranged in 8 ways.

Similarly we can arrange all the the three remaining odd integers i.e 3,5,7

16*4 = 64

we have to place 9 at the third digit.
1*8*1 = 8
first place can be arranged in one way (8)
third place can be arranged in one way (9)
second place can be arranged in 8 ways.

64+8 = 72

Let me know if you have any doubts.

Parallel_chase. That was brilliant. Thanks a lot!