Find the value of $^{100} C_{97}$

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Solution

$^{100} C_{97} = ? ⌊^{n} C_{r} = \frac{n!}{r! (n - r)!} ⌋^{100} C_{97} = \frac{100!}{97! \times 3!} = \frac{100 \times 99 \times 98}{3 \times 2 \times 1} = 161700^{60} C_{60} = 161700$
Hence the correct answer is $161700$

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