\( \dfrac{5!}{(5-r)!}= \dfrac{6!}{(6-r+1)}\)
= \( \dfrac{5!}{(5-r)!}= \dfrac{6\times 5!}{(7-r)!}\)
= \( \dfrac{5!}{(5-r)!}= \dfrac{6}{(7-r)(6-r)(5-r)!}\)
= \(1= \dfrac{6}{(7-r)(6-r)}\)
= (7 - r)(6- r)=12
= 42-6r -7r +r2=12
= (7 - r)(6- r)=6
42-6r -7r +r =6
r2 -13r +36= 0
r2 -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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