Q.
Consider, $M =2^{ a } \cdot 3^3 \cdot 7^{ c } \cdot 11^{ d }$, where $a , c , d \in N$ such that number of odd divisors of $M$ is 140 and product of all the divisors of $M$ is $( M )^{280}$.
The number of non-negative integral solutions of the inequality $x+y+z+w \leq a+c+d$ is
Permutations and Combinations
Solution: