If $^{18} C_{15} + 2 (^{18} C_{16}) +^{17} C_{16} + 1 =^{n} C_{3}$ , then n is equal to

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Solution

The correct option is B 20
$^{18} C_{15} + 2 (^{18} C_{16}) +^{17} C_{16} + 1 =^{n} C_{3}$
$^{18} C_{15} +^{18} C_{16} +^{18} C_{16} +^{17} C_{16} + 1 =^{n} C_{3}$
$[∵^{n} C_{r + 1} +^{n} C_{r} =^{n + 1} C_{r}]$
$^{19} C_{16} +^{18} C_{16} +^{17} C_{16} +^{17} C_{17} =^{n} C_{3}$
$^{19} C_{16} +^{18} C_{16} +^{18} C_{17} =^{n} C_{3}$
$^{19} C_{16} +^{19} C_{17} =^{n} C_{3}$
$^{20} C_{17} =^{n} C_{3}$
$^{20} C_{3} =^{n} C_{3}$
$\Rightarrow n = 20$ .

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