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Prove that ""^(n-1)Pr+r^(n-1)pr-1=^nPr d...

Prove that `""^(n-1)P_r+r^(n-1)p_r-1=^nP_r dot""`

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The correct Answer is:
8
`.^(n-1)P_(r )+r^(n-1)P_(r-1)=((n-1)!)/((n-1-r)!)+r((n-1)!)/((n-r)!)`
`=((n-1)!)/((n-1-r)!){1+r(1)/(n-r)}`
`=((n-1)!)/((n-1-r)!)((n)/n-r)`
`=(n!)/((n-r)!)=.^(n)P_(r )`
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