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Combinations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSCombinations3 Marks
Question
If nCp = nCp Find 12Cn.
✓

Answer

We have,
If nCp = nCq = n
Then p + q = n
Also,
${^\text{n}}\text{C}_{\text{r}}=\frac{\text{n!}}{\text{r!}(\text{n}-\text{r})!}\ ...(\text{i})$
⇒ nC4 = nC6
4 + 6 = n
⇒ n = 10
Applying (i),
${^\text{12}}\text{C}_{\text{10}}=\frac{\text{12!}}{10!2!}$
$=\frac{12\times11\times10!}{10!\times2\times1}$
$=\frac{12\times11}{2\times1}=66$

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