The positive integer r, such that  15C3r=  15Cr+3 is equal to

15c3r=  15cr+3 ⇒3r=r+3    or   3r+r+3=15      If cn,r=cn,s then either r=s or r+s=n⇒2r=3                   ⇒4r=12⇒r=32                     ⇒r=3r=32   is   not  possible since r is non negative integer⇒r=3