\( \dfrac{5!}{(5-r)!}= \dfrac{6!}{(6-r+1)}\)

= \( \dfrac{5!}{(5-r)!}= \dfrac{6\times 5!}{(7-r)!}\)

= \( \dfrac{5!}{(5-r)!}= \dfrac{6}{(7-r)(6-r)(5-r)!}\)

= \(1= \dfrac{6}{(7-r)(6-r)}\)

= (7 - r)(6- r)=12

= 42-6r -7r +r2=12

= (7 - r)(6- r)=6

42-6r -7r +r =6

r^{2} -13r +36= 0

r^{2} -4r -9r(r - 4)=0

(r - 4)(r -9)=0

= r-4=0 or r = -9 = 0

= r =4 or r =9

It is known that

\( ^6P_{r-1}=\dfrac{n!}{(n-r)!}\)'

where \( 0\leq r\leq n\)

\( 0\leq r\leq 5\)

r = 4

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