Let \( S=\{1,2,3, \ldots \ldots, 9\} \). For \( k=1,2, \ldots, 5 \), let \( \mathrm{N}_{\mathrm{...

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Let \( S=\{1,2,3, \ldots \ldots, 9\} \). For \( k=1,2, \ldots, 5 \), let \( \mathrm{N}_{\mathrm{k}} \) be the number of subsets of \( \mathrm{S} \), each containing five elements out of which exactly \( k \) are odd. Then \( \mathrm{N}_{1}+\mathrm{N}_{2}+\mathrm{N}_{3}+\mathrm{N}_{4}+\mathrm{N}_{5}= \)
(A) 210
(B) 252
(C) 125
(D) 126
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