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Example 6 (i)
Example 6 (ii)
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Example 12 (i) Important
Example 12 (ii)
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Example 24 Important
Examples
Last updated at Dec. 24, 2019 by Teachoo
Example 13 Find r, if 5 4Pr = 6 4Pr-1 Now it is given that 5 4Pr = 6 5Pr-1 5 Γ 4!/(4 β π)! = 6 Γ 5!/(5β (π β 1))! 5 Γ 4!/(4 β π)! = 6 Γ 5!/(5 β π + 1)! 5 Γ 4!/(4 β π)! = 6 Γ 5!/(6 β π)! (6 β π)!/(4 β π)! = (6 Γ 5!)/(5 Γ 4! ) ((6 β π)(5 β π)(4 β π)!)/(4 β π)! = (6 Γ 5!)/(5 Γ 4! ) (6 β r) (5 β r) = (6 Γ 5!)/(5 Γ 4! ) (6 β r) (5 β r) = (6 Γ 5 Γ 4!)/(5 Γ 4! ) (6 β r)(5 β r) = 6 6(5 β r) β r(5 β r) = 6 30 β 6r β 5r + r2 = 6 30 β 11r + r2 = 6 r2 β 11r + 30 = 6 r2 β 11r + 30 β 6 = 0 r2 β 11r + 24 = 0 r β 8r β 3r + 24 = 0 r(r - 8) β 3(r β 8) = 0 (r β 8) (r β 3) = 0 Hence r = 3, 8. But, r < n So, r < 4 and r < 5 β΄ r = 8 is not possible So, r = 3 is the answer