Among the 9 digits 1,2,3,4,5,6,7,8,9,
the 5 odd digits must appear
in the order 1,3,5,7,9, left to right
and the 4 even digits must appear
in the order 8,6,4,2,left to right
Of the 9 positions in the 9-digit number, we can choose
the 4 positions for the even digits in C(9,4) = 126 ways.
[Notice that although the even digits must be in a certain order,
order does not matter when we are picking the positions in which
the even digits will appear in the 9-digit number. For example, in
the 9-digit number 123546789 we are picking positions 2,5,6, and 8
for the even digits to go in. Notice that picking positions 5,8,2,
and 6 is the same set of positions as the set of positions 2,5,6,
and 8 or positions 8,5,6, and 2. Therefore order of POSITIONS picked
DOES NOT matter! That's why we use combinations rather than
permutations. Hope this doesn't confuse you!]
The odd digits will be placed in ascendng order in the remaining 5
positions in just C(5,5)=1 way.
Answer C(9,4) = 126 ways
Edwin
