Search any question & find its solution
Question:
Answered & Verified by Expert
If ${ }^9 C_3+{ }^9 C_5={ }^{10} C_r$ for some $r \in \mathbb{N}$, then $r=$
Options:
Solution:
2153 Upvotes
Verified Answer
The correct answer is:
$4$
${ }^n \mathrm{C}_r={ }^n \mathrm{C}_{n-r}$
$\begin{aligned} & { }^9 \mathrm{C}_5={ }^9 \mathrm{C}_4 \\ & { }^9 \mathrm{C}_3+{ }^9 \mathrm{C}_5={ }^9 \mathrm{C}_3+{ }^9 \mathrm{C}_4 \\ & ={ }^{10} \mathrm{C}_4\left(\because{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-1}={ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}}\right)\end{aligned}$
$r=4$
$\begin{aligned} & { }^9 \mathrm{C}_5={ }^9 \mathrm{C}_4 \\ & { }^9 \mathrm{C}_3+{ }^9 \mathrm{C}_5={ }^9 \mathrm{C}_3+{ }^9 \mathrm{C}_4 \\ & ={ }^{10} \mathrm{C}_4\left(\because{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-1}={ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}}\right)\end{aligned}$
$r=4$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.