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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 r is

A

3

B

4

C

5

D

8

Answer

3

Explanation

Solution

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

⇒r=3r = 3.