If ^n C_ 12 = ^n C_ 5 , Find the value of n. - Vidyadip

Question

If ${^\text{n}}\text{C}_{12}={^\text{n}}\text{C}_{5},$ Find the value of n.

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Answer

We have, ${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\frac{\mathrm{n}!}{\mathrm{r}!(\mathrm{n}-\mathrm{r})!}$ Hence, $\mathrm{n}=\mathrm{mr}=12$ and 5 Applying formula ${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{p}}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{q}}=\mathrm{n}$ Then $\mathrm{p}+\mathrm{q}=\mathrm{n}={ }^{\mathrm{n}} \mathrm{C}_{12}={ }^{\mathrm{n}} \mathrm{C}_5 12$ $+5=n \Rightarrow n=17$

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