The value of { }^{49} C_3+{ }^{48} C_3+{ }^{4 | vedclass

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Question

(A) We use the Pascal's identity: ${ }^{n} C_{r}+{ }^{n} C_{r+1}={ }^{n+1} C_{r+1}$.Given expression: ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46}

Vedclass · Accepted Answer

${ }^{50} C_4$

Vedclass · Answer

(A) We use the Pascal's identity: ${ }^{n} C_{r}+{ }^{n} C_{r+1}={ }^{n+1} C_{r+1}$.Given expression: ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$.Step $1$: Combine ${ }^{45} C_3+{ }^{45} C_4 = { }^{46} C_4$.Step $2$: Combine ${ }^{46} C_3+{ }^{46} C_4 = { }^{47} C_4$.Step $3$: Combine ${ }^{47} C_3+{ }^{47} C_4 = { }^{48} C_4$.Step $4$: Combine ${ }^{48} C_3+{ }^{48} C_4 = { }^{49} C_4$.Step $5$: Combine ${ }^{49} C_3+{ }^{49} C_4 = { }^{50} C_4$.Thus,the final value is ${ }^{50} C_4$.

The value of ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$ is

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