This quiz is about two identities involving the binomial coefficients,

2 Sum_{0..M} k ( 2M choose k ) = M 2^{2M} 4 Sum_{0..M} (M - k)^{2} ( 2M choose k ) = M 2^{2M}

k ( r choose k ) = r ( r-1 choose k-1 )

Marco Corvi - 2016