Ta có: $\sum_{k=0}^{3}k.C_{7}^{k}\textrm{}=154$
Mặt khác:
$\sum_{k=0}^{3}k.C_{7}^{k}\textrm{}+7C_{7}^{7}\textrm{}+6C_{7}^{6}\textrm{}+5C_{7}^{5}\textrm{}+4C_{7}^{4}\textrm{}=\sum_{k=0}^{7}k.C_{7}^{k}\textrm{}=7.2^{6}=7\sum_{k=0}^{3}k.C_{7}^{k}\textrm{}$.Suy ra $\sum_{k=0}^{3}k.C_{7}^{k}\textrm{}=2^{6}=64$
Từ đó suy ra 154=64?????