The value of 30C030C10 - 30C130C11 + 30C230C12 - .......... + 30C2030C30 is
30C10
Difference of suffices is same = 10 and terms are alternately positive and negative
∴ we take expansion of (1−x)30and(x+1)30 ,
multiply and equate cofficient of x20 on both sides.
(1−x)30(x+1)30=(1−x2)30
∴ coff of x20=30C10