Question #1493f

1 Answer
Alan P.
Feb 13, 2015

In general #P(a,b) = (a!)/(a-b)!#
i.e. #P(a,b) = ( a X (a-1) X (a-2) X ... X 1) / ((a-b) X (a-b-1) X ... X 1)#

Therefore
#(n - r) X P(n-1, r-1)#

# = (n-r) X (( (n-1)!)/(((n-1)-(r-1)!)))#

# = (n-r) X ( (n-1)! ) / ( ( (n-1)-(r-1) ) !)#

# = (n-r) X ( (n-1)! ) / ( (n-r) !)#

# = (n-r) X ( (n-1)! ) / ( ( (n-r) ) X (n - r -1) X (n-r-2) X ... X 1 )#

# = ( (n-1)! ) / ( (n - r -1) X (n-r-2) X ... X 1 )#

# = ( (n-1)! ) / ( ( (n-1) -r)) ! )#

#= P( (n-1), r)#

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