The Value of ^47C_4 + sum _j=1^5 ^(52-j)C_3 is equal to

(c) :We know that ^n C_r-1+ ^n C_r= ^(n+1) C_r ...(1)\ Now ^47 C_4+sum _j=1^5 ^(52-j) C_3 \ = ^40 C_4+ ^40 C_3+ ^48 C_3+ ^49 C_3+ ^50 C_3+ ^51 C_3 . \ = ^52 C_4 (using (1)). \

The value of ^47C4 + sumj = 1^5mspace2mu ^52 - jC3 is e... | Permutations and Combinations (Mathematics)

\begin{aligned} &\text { (c) :We know that }{ }^n C_{r-1}+{ }^n C_r={ }^{(n+1)} C_r \quad ...(1)\\ &\begin{aligned} & \text { Now }{ }^{47} C_4+\sum_{j=1}^5{ }^{(52-j)} C_3 \\ & ={ }^{40} C_4+{ }^{40} C_3+{ }^{48} C_3+{ }^{49} C_3+{ }^{50} C_3+{ }^{51} C_3 . \\ & ={ }^{52} C_4 \text { (using (1)). } \end{aligned} \end{aligned}

Explanation

For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

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