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Find x if nPr=x nCr - Mathematics and Statistics

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Question

Find x if `""^"n""P"_"r" = "x"  ""^"n""C"_"r"`

Sum

Solution

`""^"n""P"_"r" = "x"  ""^"n""C"_"r"`

x = `(""^"n""P"_"r")/(""^"n""C"_"r")`

= `(("n"!)/(("n" - "r")!))/(("n"!)/(("n" - "r")!"r"!))`

= `1/("r"!)`

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Properties of Combinations
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Chapter 6: Permutations and Combinations - Exercise 6.7 [Page 90]

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Balbharati Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.7 | Q 6 | Page 90

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