If n items are to arranged in a line of which r items must never be together, we can arrange them in (n-r)!r! n−r+1Crn−r+1Cr ways, provided n-r is greater than r. Can someone explain the formulae
here?

Hi Mutthu,
It say you have to choose r things from n things such that no two of them together. The same can be thought of in another way. Say you have r tings. So n-r are things are already arranged. If n-r things are arranged, there will be n-r+1 spaces. You can choose r spaces from these and put the 'r' things you have in those spaces.  Thus the required ways will be n-r+1Cr
Hope that helps.
Thanks