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JEE Math Practice Question

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

  1. A.$$\mathrm{{}^{51}{C_4} - {}^{45}{C_4}}$$
  2. B.$$\mathrm{{}^{51}{C_3} - {}^{45}{C_3}}$$
  3. C.$$\mathrm{{}^{52}{C_3} - {}^{45}{C_3}}$$
  4. D.$$\mathrm{{}^{52}{C_4} - {}^{45}{C_4}}$$

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