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Prove the following: P(n , r)=ndotP(n-1,...

Prove the following: `P(n , r)=ndotP(n-1,\ r-1)`

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We know, `n_(P_r)​=(n!​ )/((n−r)!) ..(1)`
`R.H.S. = (n−1)_(P_r)​+(n−1)_(P_(r−1))`
​=`((n−1)!​)/((n−r−1)!)+((n−1)!​)/((n−r)!)`
=`( ((n−1)!​)/((n−r−1)!)(1+r/(n−r)​)`
=` n(n−1)!​)/(((n−1)(n−r−1)!)`
=`(n!​ )/((n−r)!) ..(2)`
Hence from (1) and (2)
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