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Question
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
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Solution
`""^10"P"_("r" - 1)` = 2 × 6Pr
`(10!)/((10 - "r" + 1)!) = 2 xx (6!)/((6 -"r")!)`
`(10!)/(6! xx 2) = ((11 - "")!)/((6 - "r)!)`
`((11 - "r")(10 - "r")(9 - "r")(8 - "r")(7 - "r")(6 - "r")!)/((6 - "r")!) = (10xx 9 xx 8 xx 7 xx 6!)/(6! xx 2)`
⇒ `(11 - "r")(10 - "r")(9 - "r")(8 "r")(7 - "r") = 10 xx 9 xx 4 xx 7`
= `5 xx 2 xx 3 xx 3 xx 2 xx 2 xx 7`
= `7 xx 6 xx 5 xx 4 xx 3`
⇒ 11 – r = 7
11 – 7 = r
r = 4
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