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Combinations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSCombinations3 Marks
Question
If ${^\text{15}}\text{C}_{3\text{r}}={^\text{15}}\text{C}_{\text{r+3}},$ Find r.
✓

Answer

We have,
If nCp = nCq = n
Then p + q = n
Also,
${^\text{15}}\text{C}_{3\text{r}}={^\text{15}}\text{C}_{\text{r+3}},$
⇒ 3r + r + 3 = 15
4r + 3 = 15
4r = 15 - 3
4r = 12
r = 3

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