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Question
Find r if `""^12"P"_("r" - 2): ""^11"P"_("r" - 1)` = 3:14
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Solution
`""^12"P"_("r" - 2): ""^11"P"_("r" - 1)` = 3:14
∴ `(12!)/((12 - "r" + 2)!)÷(11!)/((11 - "r" + 1)!) = 3/14`
∴ `(12!)/((14 - "r")!) xx ((12 - "r")!)/(11!) = 3/14`
∴ `(12 xx 11!)/((14 - "r")(13 - "r")(12 - "r")!) xx ((12 - "r")!)/(11!) = 3/14`
∴ `(12)/((14 - "r")(13 - "r")) = 3/14`
∴ (14 – r) (13 – r) = 8 × 7
Comparing on both sides, we get
14 – r = 8
∴ r = 6
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