The value of $^{19} C_{18} +^{19} C_{17}$

1200

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2000

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190

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None of these

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Solution

The correct option is D $190$
$^{n} C_{r} = \frac{n!}{(n - r)! r!}$
$^{19} C_{18} +^{19} C_{17} = \frac{19!}{18!} + \frac{19!}{17! 2!}$
$= 19 + \frac{19 \times 18}{2}$
$= 19 + 171$
$= 190$

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