The product of r consecutive integers is divisible by

The product of two consecutive integers is divisible by 2. Is this statement true or false. Give Reason?

Statement-1: The smallest positive integer n such that n! can be expressed as a product of n-3 consecutive integers, is 6. Statement-2: Product of three consecutive integers is divisible by 6.

Which one of the following is the number by which the product of 8 consecutive integer is divisible ? 4 ! (b) 6 ! (c) 7 ! (d) 8 ! (e) All of these

STATEMENT-1 : The product of r consecutive integers is always divisible by r!. STATEMENT-2: The number of ways formed by utilizing all the letters of the word ASSIST in which S's are alternate , is 12. STATEMENT-3 : The number of words which can be formed out of the letters a,b,c,d,e,f taken 3 together each word containing one vowel at least is 16.

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

Consider the following statements: 1. The product of any three consecutive integers is divisible by 6. 2. Any integer can be expressed in one of the three forms 3k,3k+1,3k+2 where k is an integer Which of the above statements is/are correct

When product of r consecutive positive integers is divided by r! then the quotient is:

Prove that the product of 2n consecutive negative integers is divisible by (2n)!