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Combinations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsCombinations1 Mark
Question
Write the expression ${^\text{n}}\text{C}_{\text{r}+1}+{^\text{n}}\text{C}_{\text{r-1}}+2\times{^\text{n}}\text{C}_{\text{r}-1}$in the simplest form.
✓

Answer

${^\text{n}}\text{C}_{\text{r}+1}+{^\text{n}}\text{C}_{\text{r-1}}+2\times{^\text{n}}\text{C}_{\text{r}-1}$
$=({^\text{n}}\text{C}_{\text{r}+1}+{^\text{n}}\text{C}_{\text{r}})+​​​​{^\text{n}}\text{C}_{\text{r}}+​​​​{^\text{n}}\text{C}_{\text{r-1}}$
$={^\text{n+1}}\text{C}_{\text{r}+1}+{^\text{n+1}}\text{C}_{\text{r}}$
$={^\text{n+1+1}}\text{C}_{\text{r}+1}$
$={^\text{n+2}}\text{C}_{\text{r}+1}$

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