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The value of $\sum_{r=0}^{20} {}^{50-r}C_6$ is equal to:
(1) ${}^{51}C_7 - {}^{30}C_7$ (2) ${}^{50}C_7 - {}^{30}C_7$ (3) ${}^{50}C_6 - {}^{30}C_6$ (4) ${}^{51}C_7 + {}^{30}C_7$
Hockey stick identity: ${}^{50}C_6 + {}^{49}C_6 + \ldots + {}^{30}C_6 = {}^{51}C_7 - {}^{30}C_7$.
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