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    Which of the following statements is true ?
    Question

    Which of the following statements is true ?

    A.

    Every integer n16n\geq 16​  divides (n1)!+3(n-1)!+3 .​

    B.

    Every odd integer n16n \geq16 divides (n1)!(n-1)! .​

    C.

    Every even integer n16n \geq16​ divides (n1)!(n-1)!​ .

    D.

    For every integer n16,n2 divides n!+1n\geq 16 , n^2\ divides\ n!+1​​

    Correct option is C

    ​​Let , n = even number greater than or equal to 16 . Then, it can be written as 

    n=2×k (Where k will be some number less than n1)n=2\times k\ (\text{Where k will be some number less than }n-1) ,

    now in (n1)!(n-1)! , both 2 and k will be present so , n would easily divide (n1)!(n-1)! .​


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