If $${}^{16}{C_r} = {}^{16}{C_{r + 1}}$$, then the value of $${}^r{P_{r - 3}}$$ is

The coefficient of x^$$-$$10 in $${\left( {{x^2} - {1 \over {{x^3}}}} \right)^{10}}$$ is

Product of any r consecutive natural numbers is always divisible by

For each n $$\in$$ N, 2³ⁿ $$-$$ 1 is divisible by

here N is a set of natural numbers.