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Permutations and Combinations (p-2) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Permutations and Combinations (p-2)1 Mark
Question
Find the value of: ${ }^{15} C_4+{ }^{15} C_5$
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Answer

$
\begin{aligned}
{ }^{15} \mathrm{C}_4+{ }^{15} \mathrm{C}_5 & ={ }^{15} \mathrm{C}_5+{ }^{15} \mathrm{C}_4={ }^{15} \mathrm{C}_5+{ }^{15} \mathrm{C}_5-1 \\
& ={ }^{16} \mathrm{C}_5 \quad \ldots\left[\because \because{ }^n \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-1}={ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}}\right] \\
& =4368
\end{aligned}
$

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