If r, k, p in W, then sumlimits_{r + k + p = | vedclass

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(D) The given sum is the coefficient of $x^{10}$ in the product of the expansions of $(1+x)^{30}$,$(1+x)^{20}$,and $(1+x)^{10}$.This is equivalent to

Vedclass · Accepted Answer

$\binom{60}{10}$

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(D) The given sum is the coefficient of $x^{10}$ in the product of the expansions of $(1+x)^{30}$,$(1+x)^{20}$,and $(1+x)^{10}$.This is equivalent to the coefficient of $x^{10}$ in the expansion of $(1+x)^{30+20+10} = (1+x)^{60}$.By the binomial theorem,the coefficient of $x^{10}$ in $(1+x)^{60}$ is given by $\binom{60}{10}$.Note: The provided options in the original input were incorrect. The correct value is $\binom{60}{10}$.

If $r, k, p \in W,$ then $\sum\limits_{r + k + p = 10} {{}^{30}{C_r} \cdot {}^{20}{C_k} \cdot {}^{10}{C_p}} $ is equal to -

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