question_answer

If \[x,\ y\] and \[r\] are positive integers, then \[^{x}{{C}_{r}}{{+}^{x}}{{C}_{r-1}}^{y}{{C}_{1}}{{+}^{x}}{{C}_{r-2}}^{y}{{C}_{2}}+.......{{+}^{y}}{{C}_{r}}=\] [Karnataka CET 1993; RPET 2001]

A) \[\frac{x\ !\ y\ !}{r\ !}\]

B) \[\frac{(x+y)\ !}{r\ !}\]

C) \[^{x+y}{{C}_{r}}\]

D) \[^{xy}{{C}_{r}}\]