Q16 of 31 Page 7

Find r, if 5 4Pr = 6 5Pr-1.

5 4Pr = 6 5Pr-1







⇒ (6-r) (5-r) = 6


⇒ 30 – 6r – 5r + r2 = 6


⇒ 30 – 11r + r2 – 6 = 0


⇒ r2 –11r + 24 = 0


⇒ r2 –8r – 3r + 24 = 0


⇒ r(r-8)-3(r-8)=0


⇒ (r-8)(r-3)=0


⇒ r=8, r=3


As we know r<n,


So r<4,r<5.


∴ r = 8 is not possible.


So, r=3 is the answer.


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