Question

The product of any r consecutive natural numbers is always divisible by $r!$

• A. True
• B. False

Answer 1

The correct option is A True

Since, $r!=r(r-1)(r-2)(r-3)(r-4)(r-5)..........3\ast 2\ast 1$

and product of consecutive numbers will be $1\ast 2\ast \mathrm{3..........}(r-3)(r-2)(r-1)\left(r\right)$

Hence, product of any r consecutive natural numbers is always divisible by $r!$