The number of permutations of the set `{1, 2, 3, 4}` in which no two adjacent positions are filledby consecutive integers (increasing order)

Find the number of permutations of the set {1,2,3,4} in which no two adjacent positions are filled by consecutive integers ( increasing orders).

Find the number of r-subsets of the set S = {1, 2,.......,4} that do not contain a pair of consecutive integers.

Prove that two consecutive positive integers are always coprime.

Explain, how the product of two consecutive positive is an even integer.

The number of permutations all together of n things when r specified things are to be in an assigned order,though not necessarily consecutive is

Total number of sets of two or more consecutive positive integers having a sum of 35:

Prove that product of four consecutive positive integers increased by 1 is perfect square.

Prove that product of four consecutive positive integers increased by 1is a perfect square.

Prove that product of four consecutive positive integers increased by 1 is perfect square.