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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 13 Find r, if 5 4Pr = 6 4Pr-1 Now it is given that 5 4Pr = 6 5Pr-1 5 × 4!/(4 − 𝑟)! = 6 × 5!/(5− (𝑟 − 1))! 5 × 4!/(4 − 𝑟)! = 6 × 5!/(5 − 𝑟 + 1)! 5 × 4!/(4 − 𝑟)! = 6 × 5!/(6 − 𝑟)! (6 − 𝑟)!/(4 − 𝑟)! = (6 × 5!)/(5 × 4! ) ((6 − 𝑟)(5 − 𝑟)(4 − 𝑟)!)/(4 − 𝑟)! = (6 × 5!)/(5 × 4! ) (6 – r) (5 – r) = (6 × 5!)/(5 × 4! ) (6 – r) (5 – r) = (6 × 5 × 4!)/(5 × 4! ) (6 – r)(5 – r) = 6 6(5 – r) – r(5 – r) = 6 30 – 6r – 5r + r2 = 6 30 – 11r + r2 = 6 r2 – 11r + 30 = 6 r2 – 11r + 30 – 6 = 0 r2 – 11r + 24 = 0 r – 8r – 3r + 24 = 0 r(r - 8) – 3(r – 8) = 0 (r – 8) (r – 3) = 0 Hence r = 3, 8. But, r < n So, r < 4 and r < 5 ∴ r = 8 is not possible So, r = 3 is the answer

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.