Answer to Question #36927 in Combinatorics | Number Theory for Quamrul

Question

How many three digit numbers can be formed using the digits from 1 to 6 so that the
digits are in increasing order from left to right and for any odd digit appearing in that
number there is at least one even digit placed left to it? One digit can be used only once.

Answer 1

The first digit can be only even, as there is no digits to the left. Also, it must not be greater then 4 Hence, only two digits can be on the first place: 2 and 4. For 4, there is only one way to construct the increasing order number:

456

For 2:
256
246, 245,
234, 235, 236.

So in total we have 7 such numbers.