$\sum\limits_{k = 0}^6 {{}^{51 - k}{C_3}} $ is equal to :

Question

$\mathrm{{}^{51}{C_4} - {}^{45}{C_4}}$

$\mathrm{{}^{51}{C_3} - {}^{45}{C_3}}$

$\mathrm{{}^{52}{C_3} - {}^{45}{C_3}}$

$\mathrm{{}^{52}{C_4} - {}^{45}{C_4}}$

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