# Answer on Combinatorics | Number Theory Question for Quamrul

Question #36927

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.

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.

Expert's answer

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.

456

For 2:

256

246, 245,

234, 235, 236.

So in total we have 7 such numbers.

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