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Question: If \(15C_{3r} =^{15} ⥂ C_{r + 3}\), then the value of \(r\) is....

If 15C3r=15⥂Cr+315C_{3r} =^{15} ⥂ C_{r + 3}, then the value of rr is.

A

3

B

4

C

5

D

8

Answer

3

Explanation

Solution

15C3r=15⥂Cr+3⇒15⥂C15−3r=15⥂Cr+315C_{3r} =^{15} ⥂ C_{r + 3} \Rightarrow^{15} ⥂ C_{15 - 3r} =^{15} ⥂ C_{r + 3}

⇒15−3r=r+3⇒r=3\Rightarrow 15 - 3r = r + 3 \Rightarrow r = 3.