Question

If ⁿP_r = 840 and ⁿC_r = 35, then r = ___________.

Answer 1

Given ⁿP_r = 840 and ⁿC_r = 35
$$\begin{gathered} \mathrm{i}.\mathrm{e}\frac{n!}{\left(n-r\right)!}=840\mathrm{and}\frac{n!}{r!\left(n-r\right)!}=35 \\ \therefore \left(\frac{n!}{\left(n-r\right)!}\right)\frac{1}{r!}=35 \\ \mathrm{i}.\mathrm{e}840\left(\frac{1}{r!}\right)=35\left(\because \frac{n!}{\left(n-r\right)!}=840\mathrm{given}\right) \\ \mathrm{i}.\mathrm{e}r!=\frac{840}{35}=24 \\ =4\times 3\times 2 \\ =4! \\ \mathrm{i}.\mathrm{e}r=4 \end{gathered}$$