Prove the following

Question:

If $\mathrm{C}_{\mathrm{r}} \equiv{ }^{25} \mathrm{C}_{\mathrm{r}}$ and

$\mathrm{C}_{0}+5 \cdot \mathrm{C}_{1}+9 \cdot \mathrm{C}_{2}+\ldots \cdot+(101) \cdot \mathrm{C}_{25}=2^{25} \cdot \mathrm{k}$

then $\mathrm{k}$ is equal to________.

Solution:

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