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+1 vote
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in Combinatorics and Mathematical Induction by (46.9k points)
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Find r if 

(i) 5Pr = 2 6Pr - 1 4

(ii) 5Pr = 6Pr - 1 

1 Answer

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Best answer

(i) 5Pr = 2 6Pr - 1 4

(ii) 5Pr = 6Pr - 1 

⇒ 42 – 13r + r2 = 6 ⇒ r2 – 13r + 36 = 0 

⇒ (r – 4)(r – 9) = 0 ⇒ r = 4, 9

Now, we know that nPr is meaningful only when r ≤ n. 

5Pr and 6Pr - 1 are meaningless when r ≤ 9. 

∴ Rejecting r = 9, we have r = 4

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