A) 19
B) 20
C) 18
D) 24
E) 21
Correct Answer: B
Solution :
\[^{18}{{C}_{15}}+2{{(}^{18}}{{C}_{16}}){{+}^{17}}{{C}_{16}}+1{{=}^{n}}{{C}_{3}}\] \[\Rightarrow \] \[^{18}{{C}_{15}}{{+}^{18}}{{C}_{16}}{{+}^{18}}{{C}_{16}}{{+}^{17}}{{C}_{16}}+1{{=}^{n}}{{C}_{3}}\] \[\Rightarrow \] \[^{18}{{C}_{15}}{{+}^{18}}{{C}_{16}}{{+}^{18}}{{C}_{16}}{{+}^{17}}{{C}_{16}}{{+}^{17}}{{C}_{17}}{{=}^{n}}{{C}_{3}}\] \[\Rightarrow \] \[^{19}{{C}_{16}}{{+}^{18}}{{C}_{16}}{{+}^{18}}{{C}_{17}}{{=}^{n}}{{C}_{3}}\] \[\Rightarrow \] \[^{19}{{C}_{16}}{{+}^{19}}{{C}_{17}}{{=}^{n}}{{C}_{3}}\] \[\Rightarrow \] \[^{20}{{C}_{17}}{{=}^{n}}{{C}_{3}}\] \[\Rightarrow \] \[n=20\]
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