If nPr = 720 and nCr = 120, then the value of r is:
3
Calculation:
\(720 = \;\frac{{n!}}{{\left( {n\; - \;r} \right)!}}\)
\((n-r)! = \frac{n!}{720}\)
\(120 = \frac{{n!}}{{r!\left( {n\; - \;r} \right)!}}\)
Putting the value of (n - r)! we get
\(120 = \frac{n!}{r! \frac{n!}{720}}\)
r! = 720/120 = 6 (= 3 × 2 × 1)
r = 3
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