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?
Odd 3-digit numbers
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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.