Question

1*10C1+2*10C2+...+10*10C10=

Answer 1

1*10C1+2*10C2+...+10*10C10

=1*(10!/9!1!)+2*(10!/8!2!)+...+10*(10!/10!)

=10* [ (9!/9!) + (9!/8!1!) + ...+ (9!/9!) ]

=10* [ 9C0 + 9C1 + ...+ 9C9 ]

=10* (2^9)

=10*512

=5120