Property:Product of r consecutive number is divisible by r!

Explanation

Let r consecutive positive integers be (m).
`therefore`Product=`m(m+1)(m+2) . .. (m+r-1)`
`=((m-1)!m(m+1)(m+2) . ..(m+r-1))/((m-1)!)`
`=((m+r-1)!)/((m-1)!)=(r!*(m+r-1)!)/(r!(m-1)!)" "[because.^(m+r-1)C_(r)" is natural number"]`
`=r!*^(m+r-1)C_(r)`,
which is divisible by r!.