Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let $$\alpha$$ be the number of triangles having these points from different sides as vertices and $$\beta$$ be the number of quadrilaterals having these points from different sides as vertices. Then ($$\beta$$ $$-$$ $$\alpha$$) is equal to :

A natural number has prime factorization given by n = 2^x3^y5^z, where y and z are such
that y + z = 5 and y^$$-$$1 + z^$$-$$1 = $${5 \over 6}$$, y > z. Then the number of odd divisions of n, including 1, is :

The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is :

The total number of positive integral solutions (x, y, z) such that xyz = 24 is :