If the sum 10C_i 20C_{m_i}  is greatest then value of m  is

1)5 if u campare x^20-2m  in (1+x)³⁰

2)15 if u apply m+n c_r

3)while expanding last term 10C_m is defined for max 10 only

so what is correct one

The given thing is similar to no.of ways of selecting i elements from a 10 element set and (m-i) elements from 20 element set.That is,Selecting m elements from 30 elements set.So,the sum is equal to 30c_m which is max. iff m=15

the answer is already here... nice wrk allamraju