If ^{16 }Pr-1 : ^{15 }Pr-1 = 16 : 7 then find r.

We know that nPr = n !/( n − r )! So, 16 Pr − 1 : 15 Pr − 1 = 16 : 7 = [ 16 !/ 16 −( r − 1 )!]÷[ 15 !/ 15 −( r − 1 )]= 16 ÷ 7 16 ÷ (17 – r) = 16 ÷ 7 17 – r = 7 Hence r = 10.

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