If $^{100} C_{3} = 161700$ , then $^{100} C_{97}$ is equal to___.

53,900

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40,425

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1,61,700

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16,17,000

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Solution

The correct option is D 1,61,700
A properties of combinations is
$^{n} C_{r} =^{n} C_{r - 1}$
So, $^{100} C_{97} =^{100} C_{100 - 97} =^{100} C_{3} = 1, 61, 700$

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