2022/033) Let p be a prime and r is a number less than p. Show that $\frac{(p-1)!}{r!(p-r)!}$ is an integer

Number of ways of choosing r objects from p objects is $\frac{(p!}{r!(p-r)!}$. so $\frac{(p!}{r!(p-r)!}$ is an integer

or $\frac{p(p-1)!}{r!(p-r)!}$ is integer . Now because p does not divide the denominator  because p is prime dividing by p we get the result