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Question: Answered & Verified by Expert
If \({ }^{20} \mathrm{C}_{\mathrm{r}}={ }^{20} \mathrm{C}_{\mathrm{r}-10}\) then \({ }^{18} \mathrm{C}_{\mathrm{r}}\) is equal to
MathematicsPermutation CombinationBITSATBITSAT 2011
Options:
  • A 4896
  • B 816
  • C 1632
  • D None of these
Solution:
1006 Upvotes Verified Answer
The correct answer is: 816
\({ }^{20} \mathrm{C}_{\mathrm{r}}={ }^{20} \mathrm{C}_{\mathrm{r}-10} \Rightarrow \mathrm{r}+(\mathrm{r}-10)=20 \Rightarrow \mathrm{r}=15\)
\(\therefore \quad{ }^{18} \mathrm{C}_{\mathrm{r}}={ }^{18} \mathrm{C}_{15}={ }^{18} \mathrm{C}_3=\frac{18 \cdot 17 \cdot 16}{1 \cdot 2 \cdot 3}=816\)

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