Slide30.JPG

Slide31.JPG
Slide32.JPG

Go Ad-free

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

Davneet Singh's photo - Co-founder, Teachoo

Made by

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.