The coefficient of \( x^{50} \) in the expansion of \( \sum_{\mathrm{k}=0}^{100}{ }^{100} C_{k}(x-2)^{100-k} 3^{\mathrm{k}} \) is also equal to
\( \mathrm{P} \)
(A) number of ways in which 50 identical books can be distributed in 100 students, if each student
W can get atmost one book.
(B) number of ways in which 100 different white balls and 50 identical red balls can be arranged in a circle, if no two red balls are together.
(C) number of dissimilar terms in \( \left(\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\ldots \ldots . .+\mathrm{x}_{50}\right)^{51} \).
(D) \( \frac{2 \cdot 6 \cdot 10 \cdot 14 \cdot \ldots \ldots .198}{50 !} \)
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