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Find the product of all odd natural numbers less than 5000.
Answer & Solution
Correct Answer:
Option
B
Product of all odd natural numbers less than 5000
$$\eqalign{ & = 1 \times 3 \times 5 \times 7 \times ..... \times 4999 \cr & = \frac{{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times ... \times 5000}}{{2 \times 4 \times 6 \times 8 \times ... \times 5000}} \cr & = \frac{{5000!}}{{{2^{2500}}\left( {1 \times 2 \times 3 \times 4 \times ... \times 2500} \right)}} \cr & = \frac{{5000!}}{{{2^{2500}} \times 2500!}} \cr} $$
$$\eqalign{ & = 1 \times 3 \times 5 \times 7 \times ..... \times 4999 \cr & = \frac{{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times ... \times 5000}}{{2 \times 4 \times 6 \times 8 \times ... \times 5000}} \cr & = \frac{{5000!}}{{{2^{2500}}\left( {1 \times 2 \times 3 \times 4 \times ... \times 2500} \right)}} \cr & = \frac{{5000!}}{{{2^{2500}} \times 2500!}} \cr} $$
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