Numbers ={1,2,3,4,5,6,7,8,9}
4 digits _ _ _ _
(A)With Repetition
Case(1)unit place digit is 9.
According to 3rd condition 9 should be used exactly once.If we choose 9 for unit place then Number of choices for remaining places=8 each
Therefore no.of 4 digit numbers that can be formed= 1*8*8*8=512
Case(2) Unit place filled with 1,3,5,7
According to second condition number Should be odd.So,there are 5(1,3,5,7) choices for unit place.
Now for digit 9 there are 3 choices (2nd place or 3rd place or 4th place).and for remaining two Number of choice=8
Therefore no.of 4 digit numbers that can be formed
= 4*1*8*8 + 4*8*1*8 +4*8*8*1=768
Total 4 digit number that can be formed with repetition= 512 +768 =1280
(B)Without Repetition
Case(1)when unit place digit is 9
Number of Choice for unit Place =1
Number of Choice for 2nd Place =8
Number of Choice for 3rd Place =7
Number of Choice for 4th Place =6
Therefore no.of 4 digit numbers that can be formed= 1*8*7*6=336
Case(2)When Unit Place filled with 1,3,5,7.
Number of Choices for unit Place =4
Here 9 can come at 2nd or 3rd or 4th place.
Therefore no.of 4 digit numbers that can be formed
= 4*8*7*6=1344
Total 4 digit number that can be formed without repetition= 336 +1344 =1680